NLLoc is a nonlinear search positioning method.In this study,we use simulated arrival time data to quantitatively evaluate the NLLoc method from three aspects:arrival time picking accuracy,station distribution,and vel...NLLoc is a nonlinear search positioning method.In this study,we use simulated arrival time data to quantitatively evaluate the NLLoc method from three aspects:arrival time picking accuracy,station distribution,and velocity model.The results show that the NLLoc method exhibits high positioning accuracy and stability in terms of arrival time picking accuracy and station distribution;however,it is sensitive to the velocity model.The positioning accuracy is higher when the velocity model is smaller than the true velocity.We combined absolute and relative positioning methods.First,we use the NLLoc method for absolute positioning of seismic data and then the double difference positioning method for relative positioning to obtain a more accurate relocation result.Furthermore,we used the combined method to locate the earthquake sequence after collecting dense seismic array data on the Luanzhou M_(S)4.3 earthquake that occurred on April 16,2021,in Hebei Province.By fitting the fault plane with the relocated earthquake sequences,the results show that the strike and dip angles of the seismogenic fault of the Luanzhou M_(S)4.3 earthquake are 208.5°and 85.6°,respectively.This indicates a high-dip angle fault with North-North-East strike and North-West dip directions.Furthermore,we infer that the seismogenic fault of the Luanzhou M_(S)4.3 earthquake is the Lulong fault.展开更多
This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（...This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.展开更多
In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we ...In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.展开更多
We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;...We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;）;, f ∈ C;（[0, ∞）, R), f′（u） > 0 for u > 0, and for some 0 < β < θ such that f（u） < 0 for u ∈ [0, β)（semipositone） and f（u） > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;（[0, β） ∪（β, ∞）, R),f′′（u） ≥ 0 for u ∈ [0, β) and f′′（u） ≤ 0 for u ∈（β, ∞）, then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.展开更多
In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi｜u｜^p-2/｜x-ai｜p^u=｜u｜^p^＊-2u＋λ｜u｜^q-2u,x∈Ω,where Ω belong to R^N（N ...In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi｜u｜^p-2/｜x-ai｜p^u=｜u｜^p^＊-2u＋λ｜u｜^q-2u,x∈Ω,where Ω belong to R^N（N ≥ 3） is a smooth bounded domain such that the different points ai∈Ω,i= 1,2,...,k,0≤μi〈μ^-=（N-p/p）^p,λ〉0,1≤q〈p,and p^＊=p^N/N-p.The results depend crucially cn the parameters λ,q and μi for i=1,2,...,k.展开更多
In this paper, we consider boundary value problems for systems of nonlinear third- order differential equations. By applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams...In this paper, we consider boundary value problems for systems of nonlinear third- order differential equations. By applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem, the existence of multiple positive solutions is obtained. As application, we give some examples to demonstrate our results.展开更多
In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of mu...In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.展开更多
The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples ...The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results.展开更多
This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t&l...This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]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 study the following critical problem involving the fractional Laplacian:{(−Δ)^α/2u−γu/|x|^α=λ|u|^q−2/|x|^s+|u|^2^∗α^(t)−2u/|x|^t in Ω,u=0 in R^N∖Ω,whereΩ⊂R^N(N>α)is a bounded smooth dom...In this article,we study the following critical problem involving the fractional Laplacian:{(−Δ)^α/2u−γu/|x|^α=λ|u|^q−2/|x|^s+|u|^2^∗α^(t)−2u/|x|^t in Ω,u=0 in R^N∖Ω,whereΩ⊂R^N(N>α)is a bounded smooth domain containing the origin,α∈(0,2),0≤s,t<α,1≤q<2,λ>0,2α^*(t)=2(N-t)/N-αis the fractional critical Sobolev-Hardy exponent,0≤γ<γH,and γH is the sharp constant of the Sobolev-Hardy inequality.We deal with the existence of multiple solutions for the above problem by means of variational methods and analytic techniques.展开更多
Haze in China is primarily caused by high pollution of atmospheric fine particulates（PM2.5）.However, the detailed source structures of PM2.5 light extinction have not been well established, especially for the roles ...Haze in China is primarily caused by high pollution of atmospheric fine particulates（PM2.5）.However, the detailed source structures of PM2.5 light extinction have not been well established, especially for the roles of various organic aerosols, which makes haze management lack specified targets. This study obtained the mass concentrations of the chemical compositions and the light extinction coefficients of fine particles in the winter in Dongguan, Guangdong Province, using high time resolution aerosol observation instruments. We combined the positive matrix factor（PMF） analysis model of organic aerosols and the multiple linear regression method to establish a quantitative relationship model between the main chemical components, in particular the different sources of organic aerosols and the extinction coefficients of fine particles with a high goodness of fit（R^2= 0.953）. The results show that the contribution rates of ammonium sulphate,ammonium nitrate, biomass burning organic aerosol（BBOA）, secondary organic aerosol（SOA） and black carbon（BC） were 48.1%, 20.7%, 15.0%, 10.6%, and 5.6%, respectively. It can be seen that the contribution of the secondary aerosols is much higher than that of the primary aerosols（79.4% versus 20.6%） and are a major factor in the visibility decline. BBOA is found to have a high visibility destroying potential, with a high mass extinction coefficient, and was the largest contributor during some high pollution periods. A more detailed analysis indicates that the contribution of the enhanced absorption caused by BC mixing state was approximately 37.7% of the total particle absorption and should not be neglected.展开更多
In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′（t） ＋ p（t）x′（t） ＋ q（t）x（t） = f（t, x（t））.By using Krasnoselskii fixed point...In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′（t） ＋ p（t）x′（t） ＋ q（t）x（t） = f（t, x（t））.By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.展开更多
In this paper, existence of multiple positive solutions for fractional differential equations in Banach spaces is obtained by utilizing the fixed point index theory of completely continuous operators.
In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the crit...In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the critical fractional equation.展开更多
In this paper the existence and multiplicities of positive solutions for a class of quasiliear differential systems with singular nonlinearities via Leray Schauder degree theory are established.
In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of nonlinear neutral difference equation.The result is illustrated by an example.
In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of non-autonomous nonlinear neutral difference equation. We extend the results in [1].
In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u （t） ＋ λf （t, u） = 0, t ∈ （0, 1）, u （0） = sum （biu （ξ...In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u （t） ＋ λf （t, u） = 0, t ∈ （0, 1）, u （0） = sum （biu （ξ i ）） from i=1 to m-2, u（1）= sum （aiu（ξ i ）） from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞） and f （t, u） ≥ M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.展开更多
This paper presents sufficient conditions for the existence of positive solutions to some second-order system of difference equations subject to some boundary conditions. We show that it has at least three positive so...This paper presents sufficient conditions for the existence of positive solutions to some second-order system of difference equations subject to some boundary conditions. We show that it has at least three positive solutions under some assumptions by applying the fixed point theorem.展开更多
基金Supported by the Foundation:This research project is jointly supported by Hebei Provincial Science and Technology Program(No.22375406D)The Earthquake Science and Technology Program of Hebei Province(No.DZ2023120500009,DZ2024120500001).
文摘NLLoc is a nonlinear search positioning method.In this study,we use simulated arrival time data to quantitatively evaluate the NLLoc method from three aspects:arrival time picking accuracy,station distribution,and velocity model.The results show that the NLLoc method exhibits high positioning accuracy and stability in terms of arrival time picking accuracy and station distribution;however,it is sensitive to the velocity model.The positioning accuracy is higher when the velocity model is smaller than the true velocity.We combined absolute and relative positioning methods.First,we use the NLLoc method for absolute positioning of seismic data and then the double difference positioning method for relative positioning to obtain a more accurate relocation result.Furthermore,we used the combined method to locate the earthquake sequence after collecting dense seismic array data on the Luanzhou M_(S)4.3 earthquake that occurred on April 16,2021,in Hebei Province.By fitting the fault plane with the relocated earthquake sequences,the results show that the strike and dip angles of the seismogenic fault of the Luanzhou M_(S)4.3 earthquake are 208.5°and 85.6°,respectively.This indicates a high-dip angle fault with North-North-East strike and North-West dip directions.Furthermore,we infer that the seismogenic fault of the Luanzhou M_(S)4.3 earthquake is the Lulong fault.
基金Tutorial Scientific Research Program Foundation of Education Department of Gansu Province(0710-04).
文摘This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.
文摘In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.
文摘We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;）;, f ∈ C;（[0, ∞）, R), f′（u） > 0 for u > 0, and for some 0 < β < θ such that f（u） < 0 for u ∈ [0, β)（semipositone） and f（u） > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;（[0, β） ∪（β, ∞）, R),f′′（u） ≥ 0 for u ∈ [0, β) and f′′（u） ≤ 0 for u ∈（β, ∞）, then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.
文摘In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi｜u｜^p-2/｜x-ai｜p^u=｜u｜^p^＊-2u＋λ｜u｜^q-2u,x∈Ω,where Ω belong to R^N（N ≥ 3） is a smooth bounded domain such that the different points ai∈Ω,i= 1,2,...,k,0≤μi〈μ^-=（N-p/p）^p,λ〉0,1≤q〈p,and p^＊=p^N/N-p.The results depend crucially cn the parameters λ,q and μi for i=1,2,...,k.
基金Supported by the Shandong Provincial Natural Science Foundation(Grant No.ZR2012AQ007)Independent Innovation Foundation of Shandong University(Grant No.2012TS020)+1 种基金the Research Platform Topic of Suzhou University(Grant Nos.2012YKF332011YKF13)
文摘In this paper, we consider boundary value problems for systems of nonlinear third- order differential equations. By applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem, the existence of multiple positive solutions is obtained. As application, we give some examples to demonstrate our results.
基金The NSF (01BXL002) of Xuzhou Normal University and the NSF (03KJB110137) of Jingsu Education Committee.
文摘In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.
基金The Postdoctoral Science Research Foundation of Zhengzhou University.
文摘The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results.
基金Supported by the NSF of Guangdong Province!( 980 0 1 8) Higher Education Bureau!( 1 99873)
文摘This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]
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.
文摘In this article,we study the following critical problem involving the fractional Laplacian:{(−Δ)^α/2u−γu/|x|^α=λ|u|^q−2/|x|^s+|u|^2^∗α^(t)−2u/|x|^t in Ω,u=0 in R^N∖Ω,whereΩ⊂R^N(N>α)is a bounded smooth domain containing the origin,α∈(0,2),0≤s,t<α,1≤q<2,λ>0,2α^*(t)=2(N-t)/N-αis the fractional critical Sobolev-Hardy exponent,0≤γ<γH,and γH is the sharp constant of the Sobolev-Hardy inequality.We deal with the existence of multiple solutions for the above problem by means of variational methods and analytic techniques.
基金supported by the National Natural Science Foundation of China(Nos.41622304,U1301234)the Ministry of Science and Technology of China(Nos.2014BAC21B03,2016YFC0203600)the Science and Technology Plan of Shenzhen Municipality
文摘Haze in China is primarily caused by high pollution of atmospheric fine particulates（PM2.5）.However, the detailed source structures of PM2.5 light extinction have not been well established, especially for the roles of various organic aerosols, which makes haze management lack specified targets. This study obtained the mass concentrations of the chemical compositions and the light extinction coefficients of fine particles in the winter in Dongguan, Guangdong Province, using high time resolution aerosol observation instruments. We combined the positive matrix factor（PMF） analysis model of organic aerosols and the multiple linear regression method to establish a quantitative relationship model between the main chemical components, in particular the different sources of organic aerosols and the extinction coefficients of fine particles with a high goodness of fit（R^2= 0.953）. The results show that the contribution rates of ammonium sulphate,ammonium nitrate, biomass burning organic aerosol（BBOA）, secondary organic aerosol（SOA） and black carbon（BC） were 48.1%, 20.7%, 15.0%, 10.6%, and 5.6%, respectively. It can be seen that the contribution of the secondary aerosols is much higher than that of the primary aerosols（79.4% versus 20.6%） and are a major factor in the visibility decline. BBOA is found to have a high visibility destroying potential, with a high mass extinction coefficient, and was the largest contributor during some high pollution periods. A more detailed analysis indicates that the contribution of the enhanced absorption caused by BC mixing state was approximately 37.7% of the total particle absorption and should not be neglected.
基金The Science Research Plan(Jijiaokehezi[2016]166)of Jilin Province Education Department During the 13th Five-Year Periodthe Science Research Starting Foundation(2015023)of Jilin Agricultural University
文摘In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′（t） ＋ p（t）x′（t） ＋ q（t）x（t） = f（t, x（t））.By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.
基金Supported by the Foundation for Outstanding Middle-Aged and Young Scientists of Shandong Province(Grant No.BS2010SF004)the National Natural Science Foundation of China(Grant No.10971179)+2 种基金a Project of Shandong Province Higher Educational Science and Technology Program(Grant Nos.J10LA53J11LA02)the Natural Science Foundation of Liaocheng University(Grant No.X09008)
文摘In this paper, existence of multiple positive solutions for fractional differential equations in Banach spaces is obtained by utilizing the fixed point index theory of completely continuous operators.
基金supported by National Natural Science Foundation of China(11871315)Natural Science Foundation of Shanxi Province of China(201901D111021)。
文摘In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the critical fractional equation.
文摘In this paper the existence and multiplicities of positive solutions for a class of quasiliear differential systems with singular nonlinearities via Leray Schauder degree theory are established.
文摘In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of nonlinear neutral difference equation.The result is illustrated by an example.
文摘In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of non-autonomous nonlinear neutral difference equation. We extend the results in [1].
基金Supported by Fund of National Natural Science of China (No. 10371068)Science Foundation of Business College of Shanxi University (No. 2008053)
文摘In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u （t） ＋ λf （t, u） = 0, t ∈ （0, 1）, u （0） = sum （biu （ξ i ）） from i=1 to m-2, u（1）= sum （aiu（ξ i ）） from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞） and f （t, u） ≥ M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.
基金The project was supported by the Natural Science Foundation of Hebei Province (A2006000298)the Doctoral Program Foundation of Hebei Province (B2004204).
文摘This paper presents sufficient conditions for the existence of positive solutions to some second-order system of difference equations subject to some boundary conditions. We show that it has at least three positive solutions under some assumptions by applying the fixed point theorem.
