Using NCEP/NCAR daily reanalysis data and SCSMEX data, an investigation is carried out of the relationship between the position variation of the west Pacific subtropical high （WPSH） and the apparcnt heating in June ...Using NCEP/NCAR daily reanalysis data and SCSMEX data, an investigation is carried out of the relationship between the position variation of the west Pacific subtropical high （WPSH） and the apparcnt heating in June 1998 based on the complete vertical vorticlty equation. It is tbund that the non-adiabatic heating plays an important role in the position variation of WPSH. In comparison with climatic mean status, the vertical change of non-adiabatic heating is stronger in the north side of WPSH in June 1998, but weaker in the south side of WPSH. The anomalous non-uniform heating induces anomalous cyclonic vorticity in South China, areas to lhe south of the Yangtze and its mid-lower valleys, but anomalous anticyclonic vorticity in the Indo-China Peninsula and South China Sea areas lead to the more southward position of WPSH than the mean.展开更多
The accumulation dynamics of kernel components for spikelets at different positions within a rice panicle were investigated during grain filling to understand the physiological reasons for the variation of grain quali...The accumulation dynamics of kernel components for spikelets at different positions within a rice panicle were investigated during grain filling to understand the physiological reasons for the variation of grain quality.Two rice cultivars,Yangdao 6 （indica） and Yangjing 9538 （japonica）,were field-grown,and the grain filling characters and contents of starch,soluble sugar,and protein of the spikelets at different positions were studied.There were significant differences in matter accumulation among spikelets at different positions during grain filling.The early-flowering spikelets presented dominance over the late-flowering spikelets in initial time and initial rate of accumulation.At the initial and mid filling stages,the contents and the rates of starch and amylose accumulation in spikelets decreased with the flowering sequence,but soluble sugar content （SSC） exhibited the opposite trend.The difference in SSC among the spikelets of Yangjing 9538 was greater than that of Yangdao 6,but amylose content in mature spikelets showed no obvious relationship to their flowering sequence.The crude protein content （CPC） of early-flowering spikelets decreased more rapidly than that of late-flowering ones at the initial filling stage,and CPC in the spikelets on the secondary branch was higher than that on the primary branch,but CPC in early-flowering ones was lower than that in late-flowering across the whole grain filling period.Grain water content （GWC） of early-flowering spikelets decreased more rapidly than that of late-flowering spikelets on the same branch at the initial and mid filling stages,especially for the top grain on each primary branch.The results suggested that poor grain filling of late-flowering spikelets may be attributed to their low biological activity rather than carbohydrate supply limitation.展开更多
The measurement of atmospheric water vapor （WV） content and variability is important for meteorological and climatological research. A technique for the remote sensing of atmospheric WV content using ground-based Gl...The measurement of atmospheric water vapor （WV） content and variability is important for meteorological and climatological research. A technique for the remote sensing of atmospheric WV content using ground-based Global Positioning System （GPS） has become available, which can routinely achieve accuracies for integrated WV content of 1-2 kg/m2. Some experimental work has shown that the accuracy of WV measurements from a moving platform is comparable to that of （static） land-based receivers. Extending this technique into the marine environment on a moving platform would be greatly beneficial for many aspects of meteorological research, such as the calibration of satellite data, investigation of the air-sea interface, as well as forecasting and climatological studies. In this study, kinematic precise point positioning has been developed to investigate WV in the Arctic Ocean （80°-87°N） and annual variations are obtained for 2008 and 2012 that are identical to those related to the enhanced greenhouse effect.展开更多
At present,GNSS-Acoustic(GNSS-A)combined technology is widely used in positioning for seafloor geodetic stations.Based on Sound Velocity Profiles(SVPs)data,the equal gradient acoustic ray-tracing method is applied in ...At present,GNSS-Acoustic(GNSS-A)combined technology is widely used in positioning for seafloor geodetic stations.Based on Sound Velocity Profiles(SVPs)data,the equal gradient acoustic ray-tracing method is applied in high-precision position inversion.However,because of the discreteness of the SVPs used in the forementioned method,it ignores the continuous variation of sound velocity structure in time domain,which worsens the positioning accuracy.In this study,the time-domain variation of Sound Speed Structure(SSS)has been considered,and the cubic B-spline function is applied to characterize the perturbed sound velocity.Based on the ray-tracing theory,an inversion model of“stepwise iteration&progressive corrections”for both positioning and sound speed information is proposed,which conducts the gradual correction of seafloor geodetic station coordinates and disturbed sound velocity.The practical data was used to test the effectiveness of our method.The results show that the Root Mean Square(RMS)errors of the residual values of the traditional methods without sound velocity correction,based on quadratic polynomial correction and based on cubic B-spline function correction are 1.43 ms,0.44 ms and 0.21 ms,respectively.The inversion model with sound velocity correction can effectively eliminate the systematic error caused by the change of SSS,and significantly improve the positioning accuracy of the seafloor geodetic stations.展开更多
Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outli...Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outliers,or unknown and time-varying noise statistical characteristics,a robust SLAM method based on the improved variational Bayesian adaptive Kalman filtering(IVBAKF)is proposed.First,the measurement noise covariance is estimated using the variable Bayesian adaptive filtering algorithm.Then,the estimated covariance matrix is robustly processed through the weight function constructed in the form of a reweighted average.Finally,the system updates are iterated multiple times to further gradually correct the state estimation error.Furthermore,to observe features at different depths,a feature measurement model containing depth parameters is constructed.Experimental results show that when the measurement noise does not obey the Gaussian distribution and there are outliers in the measurement information,compared with the variational Bayesian adaptive SLAM method,the positioning accuracy of the proposed method is improved by 17.23%,20.46%,and 17.76%,which has better applicability and robustness to environmental disturbance.展开更多
BACKGROUND Meralgia paresthetica(MP)is an entrapment mononeuropathy of the lateral femoral cutaneous nerve(LFCN).Although structural abnormalities in nerve tissues can be confirmed using ultrasonography,this is not ro...BACKGROUND Meralgia paresthetica(MP)is an entrapment mononeuropathy of the lateral femoral cutaneous nerve(LFCN).Although structural abnormalities in nerve tissues can be confirmed using ultrasonography,this is not routinely performed.CASE SUMMARY Herein,we present the case of a 52-year-old woman who developed MP after laparoscopic gynecological surgery.The patient was referred to our clinic from an obstetrics and gynecology clinic with symptoms of numbness and a tingling sensation in the left anterolateral thigh,which developed after surgery performed 5 mo earlier.Tests were performed to assess the disease status and determine the underlying causes.Ultrasonographic examination revealed an anatomical variation,where the left LFCN was entrapped within the inguinal ligament.This case suggests that performing ultrasonographic examination before and after surgery in the lithotomy position could help prevent MP.CONCLUSION This case demonstrates the value of ultrasonography in detecting anatomical variation and diagnosing persistent MP.Ultrasonography should be considered an adjunct to electromyography for optimal MP management.Further,this case would help other clinicians determine patient prognosis and decide on targeted treatment strategies.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p...In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p≤q<p^(3)=3p/3-p and △_(p)u=div(|▽u|^(p-2)▽u)Under certain assumptions on the functions l and h, we employ the mountain pass theorem to establish the existence of positive solutions for this system.展开更多
This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation b...This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.展开更多
In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where ...In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.展开更多
In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems {-△u＋u=（1＋a（x））｜u｜P-1u＋μ｜u｜a-2u｜v｜β＋λv in Rn,-△u＋u=（1＋b（x））｜v｜p-1v＋μ｜u｜a｜...In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems {-△u＋u=（1＋a（x））｜u｜P-1u＋μ｜u｜a-2u｜v｜β＋λv in Rn,-△u＋u=（1＋b（x））｜v｜p-1v＋μ｜u｜a｜v｜β-2v＋λu in Rn To find nontrivial solutions, we first investigate autonomous systems. In this case, results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem. Next, the existence of positive solutions of problem （0.1） is obtained by variational methods.展开更多
This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exp...This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exponent,λ>0,p(?)r<p,p:=Np/N-p is the critical Sobolev exponent,μ>,0(?)t<p,p(?)q<p(t)=p(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.展开更多
In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an op...In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an open bounded domain with smooth boundary, 1 〈 q 〈 2, λ 〉 0. 2＊= 2N/N-2 is the critical Sobolev exponent, f ∈L2＊/2N/N-2 is nonzero and nonnegative, and g E （Ω） is a positive function with k local maximum points. By the Nehari method and variational method, k ＋ 1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75（2012） 2660-26711.展开更多
In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at ...In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.展开更多
In this paper,we study a coupled fourth-order system of Kirchhoff type.Under appropriate hypotheses of V_(i)(x)for i=1,2,f and g,we obtained two main existence theorems of weak solutions for the problem by variational...In this paper,we study a coupled fourth-order system of Kirchhoff type.Under appropriate hypotheses of V_(i)(x)for i=1,2,f and g,we obtained two main existence theorems of weak solutions for the problem by variational methods.Some recent results are extended.展开更多
基金Innovation Plans for Postgraduates of Higher Education Colleges in Jiangsu Province(E30000008098-3)Natural Science Foundation of China (40575045)+1 种基金National Key Fundamental ResearchDevelopment Plans (2004CB418302 2004CB418303)
文摘Using NCEP/NCAR daily reanalysis data and SCSMEX data, an investigation is carried out of the relationship between the position variation of the west Pacific subtropical high （WPSH） and the apparcnt heating in June 1998 based on the complete vertical vorticlty equation. It is tbund that the non-adiabatic heating plays an important role in the position variation of WPSH. In comparison with climatic mean status, the vertical change of non-adiabatic heating is stronger in the north side of WPSH in June 1998, but weaker in the south side of WPSH. The anomalous non-uniform heating induces anomalous cyclonic vorticity in South China, areas to lhe south of the Yangtze and its mid-lower valleys, but anomalous anticyclonic vorticity in the Indo-China Peninsula and South China Sea areas lead to the more southward position of WPSH than the mean.
基金supported by the National Natural Science Foundation of China(Grant Nos.30400276 and 30871480)the National Natural Science Foundation of Major International Cooperation Project(Grant No.31061140457)+1 种基金the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2009005)the Scientific Research Foundation for the Talents of Jiangsu Province,China
文摘The accumulation dynamics of kernel components for spikelets at different positions within a rice panicle were investigated during grain filling to understand the physiological reasons for the variation of grain quality.Two rice cultivars,Yangdao 6 （indica） and Yangjing 9538 （japonica）,were field-grown,and the grain filling characters and contents of starch,soluble sugar,and protein of the spikelets at different positions were studied.There were significant differences in matter accumulation among spikelets at different positions during grain filling.The early-flowering spikelets presented dominance over the late-flowering spikelets in initial time and initial rate of accumulation.At the initial and mid filling stages,the contents and the rates of starch and amylose accumulation in spikelets decreased with the flowering sequence,but soluble sugar content （SSC） exhibited the opposite trend.The difference in SSC among the spikelets of Yangjing 9538 was greater than that of Yangdao 6,but amylose content in mature spikelets showed no obvious relationship to their flowering sequence.The crude protein content （CPC） of early-flowering spikelets decreased more rapidly than that of late-flowering ones at the initial filling stage,and CPC in the spikelets on the secondary branch was higher than that on the primary branch,but CPC in early-flowering ones was lower than that in late-flowering across the whole grain filling period.Grain water content （GWC） of early-flowering spikelets decreased more rapidly than that of late-flowering spikelets on the same branch at the initial and mid filling stages,especially for the top grain on each primary branch.The results suggested that poor grain filling of late-flowering spikelets may be attributed to their low biological activity rather than carbohydrate supply limitation.
基金Chinese Polar Environment Comprehensive Investigation and Assessment Programmes under contract Nos CHINARE2013-03-03 and CHINARE 2013-04-03the National Oceanic Commonweal Research Project under contract No.201105001the National Natural Science Foundation of China under contract No.41374043
文摘The measurement of atmospheric water vapor （WV） content and variability is important for meteorological and climatological research. A technique for the remote sensing of atmospheric WV content using ground-based Global Positioning System （GPS） has become available, which can routinely achieve accuracies for integrated WV content of 1-2 kg/m2. Some experimental work has shown that the accuracy of WV measurements from a moving platform is comparable to that of （static） land-based receivers. Extending this technique into the marine environment on a moving platform would be greatly beneficial for many aspects of meteorological research, such as the calibration of satellite data, investigation of the air-sea interface, as well as forecasting and climatological studies. In this study, kinematic precise point positioning has been developed to investigate WV in the Arctic Ocean （80°-87°N） and annual variations are obtained for 2008 and 2012 that are identical to those related to the enhanced greenhouse effect.
基金National Natural Science Foundation of China(Nos.41931076,42174020)Laoshan Laboratory(No.LSKJ202205101)State Key Laboratory of Geo-Information Engineering(No.SKLGIE2020-M-1-1)。
文摘At present,GNSS-Acoustic(GNSS-A)combined technology is widely used in positioning for seafloor geodetic stations.Based on Sound Velocity Profiles(SVPs)data,the equal gradient acoustic ray-tracing method is applied in high-precision position inversion.However,because of the discreteness of the SVPs used in the forementioned method,it ignores the continuous variation of sound velocity structure in time domain,which worsens the positioning accuracy.In this study,the time-domain variation of Sound Speed Structure(SSS)has been considered,and the cubic B-spline function is applied to characterize the perturbed sound velocity.Based on the ray-tracing theory,an inversion model of“stepwise iteration&progressive corrections”for both positioning and sound speed information is proposed,which conducts the gradual correction of seafloor geodetic station coordinates and disturbed sound velocity.The practical data was used to test the effectiveness of our method.The results show that the Root Mean Square(RMS)errors of the residual values of the traditional methods without sound velocity correction,based on quadratic polynomial correction and based on cubic B-spline function correction are 1.43 ms,0.44 ms and 0.21 ms,respectively.The inversion model with sound velocity correction can effectively eliminate the systematic error caused by the change of SSS,and significantly improve the positioning accuracy of the seafloor geodetic stations.
基金Primary Research and Development Plan of Jiangsu Province(No.BE2022389)Jiangsu Province Agricultural Science and Technology Independent Innovation Fund Project(No.CX(22)3091)the National Natural Science Foundation of China(No.61773113)。
文摘Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outliers,or unknown and time-varying noise statistical characteristics,a robust SLAM method based on the improved variational Bayesian adaptive Kalman filtering(IVBAKF)is proposed.First,the measurement noise covariance is estimated using the variable Bayesian adaptive filtering algorithm.Then,the estimated covariance matrix is robustly processed through the weight function constructed in the form of a reweighted average.Finally,the system updates are iterated multiple times to further gradually correct the state estimation error.Furthermore,to observe features at different depths,a feature measurement model containing depth parameters is constructed.Experimental results show that when the measurement noise does not obey the Gaussian distribution and there are outliers in the measurement information,compared with the variational Bayesian adaptive SLAM method,the positioning accuracy of the proposed method is improved by 17.23%,20.46%,and 17.76%,which has better applicability and robustness to environmental disturbance.
文摘BACKGROUND Meralgia paresthetica(MP)is an entrapment mononeuropathy of the lateral femoral cutaneous nerve(LFCN).Although structural abnormalities in nerve tissues can be confirmed using ultrasonography,this is not routinely performed.CASE SUMMARY Herein,we present the case of a 52-year-old woman who developed MP after laparoscopic gynecological surgery.The patient was referred to our clinic from an obstetrics and gynecology clinic with symptoms of numbness and a tingling sensation in the left anterolateral thigh,which developed after surgery performed 5 mo earlier.Tests were performed to assess the disease status and determine the underlying causes.Ultrasonographic examination revealed an anatomical variation,where the left LFCN was entrapped within the inguinal ligament.This case suggests that performing ultrasonographic examination before and after surgery in the lithotomy position could help prevent MP.CONCLUSION This case demonstrates the value of ultrasonography in detecting anatomical variation and diagnosing persistent MP.Ultrasonography should be considered an adjunct to electromyography for optimal MP management.Further,this case would help other clinicians determine patient prognosis and decide on targeted treatment strategies.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
文摘In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p≤q<p^(3)=3p/3-p and △_(p)u=div(|▽u|^(p-2)▽u)Under certain assumptions on the functions l and h, we employ the mountain pass theorem to establish the existence of positive solutions for this system.
基金Supported by Research Start-up Fund of Jianghan University(06050001).
文摘This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.
基金supported by Natural Science Foundation of China(11371159 and 11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT_17R46
文摘In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.
基金supported by National Natural Science Foundations of China(10631030,10961016)
文摘In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems {-△u＋u=（1＋a（x））｜u｜P-1u＋μ｜u｜a-2u｜v｜β＋λv in Rn,-△u＋u=（1＋b（x））｜v｜p-1v＋μ｜u｜a｜v｜β-2v＋λu in Rn To find nontrivial solutions, we first investigate autonomous systems. In this case, results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem. Next, the existence of positive solutions of problem （0.1） is obtained by variational methods.
基金This research is supported by the National Natural Science Foundation of China(l0171036) and the Natural Science Foundation of South-Central University For Nationalities(YZZ03001).
文摘This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exponent,λ>0,p(?)r<p,p:=Np/N-p is the critical Sobolev exponent,μ>,0(?)t<p,p(?)q<p(t)=p(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.
基金Supported by National Natural Science Foundation of China(11471267)the Doctoral Scientific Research Funds of China West Normal University(15D006 and 16E014)+1 种基金Meritocracy Research Funds of China West Normal University(17YC383)Natural Science Foundation of Education of Guizhou Province(KY[2016]046)
文摘In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an open bounded domain with smooth boundary, 1 〈 q 〈 2, λ 〉 0. 2＊= 2N/N-2 is the critical Sobolev exponent, f ∈L2＊/2N/N-2 is nonzero and nonnegative, and g E （Ω） is a positive function with k local maximum points. By the Nehari method and variational method, k ＋ 1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75（2012） 2660-26711.
文摘In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.
基金Supported by National Natural Science Foundation of China(Grant No.11671403,11671236)。
文摘In this paper,we study a coupled fourth-order system of Kirchhoff type.Under appropriate hypotheses of V_(i)(x)for i=1,2,f and g,we obtained two main existence theorems of weak solutions for the problem by variational methods.Some recent results are extended.
