Conservation law plays a very important role in many geometric variational problems and related elliptic systems.In this note,we refine the conservation law obtained by Lamm-Rivière for fourth order systems and d...Conservation law plays a very important role in many geometric variational problems and related elliptic systems.In this note,we refine the conservation law obtained by Lamm-Rivière for fourth order systems and de Longueville-Gastel for general even order systems.展开更多
This paper deals with even order nonlinear differential equations. Applying the Schauder fixed point theorem and the Schwartz inequality technique, we give a criterion to ensure the existence and uniqueness of periodi...This paper deals with even order nonlinear differential equations. Applying the Schauder fixed point theorem and the Schwartz inequality technique, we give a criterion to ensure the existence and uniqueness of periodic solutions. This criterion is a complement of the well known Lazer type results.展开更多
In this short note,we establish a sharp Morrey regularity theory for an even order elliptic system of Rivière type:△^(m)u=∑_(t=0)^(m-1)△^(l)<Vl,du>+∑_(t=0)^(m-2)△^(l)δ(ω_(l)du)+f in B^(2m)under minim...In this short note,we establish a sharp Morrey regularity theory for an even order elliptic system of Rivière type:△^(m)u=∑_(t=0)^(m-1)△^(l)<Vl,du>+∑_(t=0)^(m-2)△^(l)δ(ω_(l)du)+f in B^(2m)under minimal regularity assumptions on the coefficients functions Vl,wl and that f belongs to certain Morrey space.This can be regarded as a further extension of the recent Lp-regularity theory obtained by Guo–Xiang–Zheng[J.Math.Pures Appl.(9),165,286–324(2022)],and generalizes[Proc.Amer.Math.Soc.,152(10),4261–4268(2024)],[Acta Math.Sci.Ser.B(Engl.Ed.),44(2),420–430(2024)]for second and fourth order elliptic systems.展开更多
Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improv...Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.展开更多
By using the integral averaging technique, oscillating criteria for certain even order neutral differential equation with deviating arguments are established. These results extend some known oscillation criteria due t...By using the integral averaging technique, oscillating criteria for certain even order neutral differential equation with deviating arguments are established. These results extend some known oscillation criteria due to Xu and Xia.展开更多
By Riccati transformation, we establish some new oscillation criteria for a class of even order delay differential equations with nonlinear term. In some sense, the results obtained extend some known results in the li...By Riccati transformation, we establish some new oscillation criteria for a class of even order delay differential equations with nonlinear term. In some sense, the results obtained extend some known results in the literature.展开更多
In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and...In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and the technique of differential inequalities, some new sufficient conditions are obtained for the oscillation of the partial differential equations under Robin boundary value conditions. The results generalize some of the previous results.展开更多
In this paper,we shall consider a class of even order mixed neutral differential equations. Some new oscillations criteria of the solutions are obtained.
We calculated the harmonic spectra generated from the asymmetric molecules of HD^＋ and HeH^2＋. It is found that HD＋produces only odd harmonics, while HeH^2＋produces both odd and even harmonics. Further analysis re...We calculated the harmonic spectra generated from the asymmetric molecules of HD^＋ and HeH^2＋. It is found that HD＋produces only odd harmonics, while HeH^2＋produces both odd and even harmonics. Further analysis reveals that for both HD^＋ and HeH^2＋, the nuclear dipole acceleration can generate even harmonics, but it is three orders of magnitude lower than that of the electron. Hence, the electronic dipole acceleration dominates the harmonic generation. For HD^＋,the electronic dipole acceleration only contributes to the generation of odd harmonics, but for HeH^2＋it contributes to the generation of both odd and even harmonics. Besides, one concept of the broken degree of system-symmetry is proposed to explain the different odd-even property between the harmonic spectra of HD^＋ and HeH^2＋.展开更多
Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtai...Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.展开更多
基金supported by the Young Scientist Program of the Ministry of Science and Technology of China(2021YFA1002200)the National Natural Science Foundation of China(12101362)+4 种基金the Natural Science Foundation of Shandong Province(ZR2021QA003)supported by the National Natural Science Foundation of China(12271296)the Natural Science Foundation of Hubei Province(2024AFA061)supported by the National Natural Science Foundation of China(11571131)the Open Research Fund of Key Laboratory of Nonlinear Analysis&Applications(Central China Normal University),Ministry of Education,P.R.China。
文摘Conservation law plays a very important role in many geometric variational problems and related elliptic systems.In this note,we refine the conservation law obtained by Lamm-Rivière for fourth order systems and de Longueville-Gastel for general even order systems.
文摘This paper deals with even order nonlinear differential equations. Applying the Schauder fixed point theorem and the Schwartz inequality technique, we give a criterion to ensure the existence and uniqueness of periodic solutions. This criterion is a complement of the well known Lazer type results.
基金Supported by the Young Scientist Program of the Ministry of Science and Technology of China(Grant No.2021Y-FA1002200)the National Natural Science Foundation of China(Grant No.12101362)the Tai-Shan Scholar Program and the Natural Science Foundation of Shandong Province(Grant Nos.ZR2022YQ01,ZR2021QA003)。
文摘In this short note,we establish a sharp Morrey regularity theory for an even order elliptic system of Rivière type:△^(m)u=∑_(t=0)^(m-1)△^(l)<Vl,du>+∑_(t=0)^(m-2)△^(l)δ(ω_(l)du)+f in B^(2m)under minimal regularity assumptions on the coefficients functions Vl,wl and that f belongs to certain Morrey space.This can be regarded as a further extension of the recent Lp-regularity theory obtained by Guo–Xiang–Zheng[J.Math.Pures Appl.(9),165,286–324(2022)],and generalizes[Proc.Amer.Math.Soc.,152(10),4261–4268(2024)],[Acta Math.Sci.Ser.B(Engl.Ed.),44(2),420–430(2024)]for second and fourth order elliptic systems.
文摘Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.
文摘By using the integral averaging technique, oscillating criteria for certain even order neutral differential equation with deviating arguments are established. These results extend some known oscillation criteria due to Xu and Xia.
文摘By Riccati transformation, we establish some new oscillation criteria for a class of even order delay differential equations with nonlinear term. In some sense, the results obtained extend some known results in the literature.
基金Supported by Guangdong Province Teaching Reform Project in Higher Education(GDJG20142396)Higher School Characteristic Innovation Project(research in education)of Guangdong Province in 2014
文摘In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and the technique of differential inequalities, some new sufficient conditions are obtained for the oscillation of the partial differential equations under Robin boundary value conditions. The results generalize some of the previous results.
文摘In this paper,we shall consider a class of even order mixed neutral differential equations. Some new oscillations criteria of the solutions are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11404153,11135002,11475076,and 11405077)the Fundamental Research Funds for the Central Universities of China(Grants Nos.lzujbky-2016-29,lzujbky-2016-31,and lzujbky-2016-209)
文摘We calculated the harmonic spectra generated from the asymmetric molecules of HD^＋ and HeH^2＋. It is found that HD＋produces only odd harmonics, while HeH^2＋produces both odd and even harmonics. Further analysis reveals that for both HD^＋ and HeH^2＋, the nuclear dipole acceleration can generate even harmonics, but it is three orders of magnitude lower than that of the electron. Hence, the electronic dipole acceleration dominates the harmonic generation. For HD^＋,the electronic dipole acceleration only contributes to the generation of odd harmonics, but for HeH^2＋it contributes to the generation of both odd and even harmonics. Besides, one concept of the broken degree of system-symmetry is proposed to explain the different odd-even property between the harmonic spectra of HD^＋ and HeH^2＋.
基金supported by the National Natural Science Foundation of China (Grant No 10574060)the Natural Science Foundation of Shandong Province, China (Grant No Y2008A23)
文摘Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.
