The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems ar...The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied.展开更多
This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corr...This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.展开更多
In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions ...In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.展开更多
In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Pal...In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Palais-Smale sequences created from related approximation problems,the existence of infinitely many solutions to the system is established.展开更多
目的当前大多数的混沌图像加密算法采用与明文相关的对称加密方式,存在密钥冗余以及一次一密模式难以实现的问题,为此,提出一种新的椭圆曲线与自适应DNA(deoxyribonucleic acid)编码结合的混沌图像加密算法。方法算法利用椭圆曲线的公...目的当前大多数的混沌图像加密算法采用与明文相关的对称加密方式,存在密钥冗余以及一次一密模式难以实现的问题,为此,提出一种新的椭圆曲线与自适应DNA(deoxyribonucleic acid)编码结合的混沌图像加密算法。方法算法利用椭圆曲线的公钥密码体制达成密钥共识,结合4维Lorenz超混沌系统产生共识密钥序列用于自适应DNA编码加密,在DNA编解码的扩散过程中内嵌中间密文状态反馈的动态扩散—自适应置换结构以抵抗分割攻击与选择明文攻击,加密过程的密文状态在解密端能够自适应同步,无需额外传输。结果算法的密钥空间为2256,足以抵抗穷举攻击。通过对多幅不同尺寸的测试图像进行仿真,比特变化率(number of bit change rate,NBCR)均接近50%,密文各方向上的相邻像素相关性均接近于0,信息熵接近理想值8,并且全部通过NIST SP800-22随机性测试以及抗差分攻击分析。其他混沌图像加密算法进行对比分析,结果表明,本文算法具有极高的实用性和安全性。结论本文算法完善了密钥冗余的问题,提高了算法的可行性,同时通过实验验证了算法的安全性,适合用于对各种尺寸的图像进行加密及相关的信息安全保障。展开更多
In this article, an elliptic system is investigated, which involves Hardy-type potentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argu...In this article, an elliptic system is investigated, which involves Hardy-type potentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argument, the Palais-Smale sequences of related approximation problems is analyzed and the existence of infinitely many solutions to the system is established.展开更多
In this paper, we study the planar Hamiltonian systemwhere where f is real analytic in x and θ,A（θ） is a 2×2real analytic symmetric matrix,J=（1^-1） and w is a Diophantine vector. Under the assumption that t...In this paper, we study the planar Hamiltonian systemwhere where f is real analytic in x and θ,A（θ） is a 2×2real analytic symmetric matrix,J=（1^-1） and w is a Diophantine vector. Under the assumption that the unperturbed systemreducible and stable, we obtain a series of criteria for the stability and instability of the equilibrium of the perturbed system.展开更多
This paper is concerned with ground states of two-component trapped Bose-Einstein condensates passing an obstacle in R^(2),where the intraspecies interactions are attractive and the interspecies interactions are repul...This paper is concerned with ground states of two-component trapped Bose-Einstein condensates passing an obstacle in R^(2),where the intraspecies interactions are attractive and the interspecies interactions are repulsive.We address the classification on the existence and non-existence of ground states.The limiting profiles of ground states are also studied by the energy analysis and the elliptic partial differential equation theory.展开更多
In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system {Sk1（λ（D2u1））＋a1（｜x｜）｜△u1｜k1=p1（｜x｜）f1（u2） for x∈RN,Sk2（λ...In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system {Sk1（λ（D2u1））＋a1（｜x｜）｜△u1｜k1=p1（｜x｜）f1（u2） for x∈RN,Sk2（λ（D2u2））＋a2（｜x｜）｜△u2｜k2=p2（｜x｜）f2（u1） for x∈RN.Here Ski （λ （D2ui）） is the ki-Hessian operator, a1, p1, f1, a2, p2 and f2 are continuous functions.展开更多
The singularly perturbed problems for elliptic systems are considered. Undersuitable conditions, using the comparison theorem the asymptotic behavior of solution forthe boundary value problems are studied.
This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nire...This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.展开更多
基金The project supported by the National Natural Science Foundation of China
文摘The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied.
基金supported by National Natural Science Foundation of China (Grant No. 10771219, 11071092)the PhD Specialized Grant of the Ministry of Education of China (Grant No. 20100144110001)
文摘This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.
文摘In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.10771219 and 11071092)the PhD Specialized Grant of the Ministry of Education of China(Grant No.20110144110001)
文摘In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Palais-Smale sequences created from related approximation problems,the existence of infinitely many solutions to the system is established.
文摘目的当前大多数的混沌图像加密算法采用与明文相关的对称加密方式,存在密钥冗余以及一次一密模式难以实现的问题,为此,提出一种新的椭圆曲线与自适应DNA(deoxyribonucleic acid)编码结合的混沌图像加密算法。方法算法利用椭圆曲线的公钥密码体制达成密钥共识,结合4维Lorenz超混沌系统产生共识密钥序列用于自适应DNA编码加密,在DNA编解码的扩散过程中内嵌中间密文状态反馈的动态扩散—自适应置换结构以抵抗分割攻击与选择明文攻击,加密过程的密文状态在解密端能够自适应同步,无需额外传输。结果算法的密钥空间为2256,足以抵抗穷举攻击。通过对多幅不同尺寸的测试图像进行仿真,比特变化率(number of bit change rate,NBCR)均接近50%,密文各方向上的相邻像素相关性均接近于0,信息熵接近理想值8,并且全部通过NIST SP800-22随机性测试以及抗差分攻击分析。其他混沌图像加密算法进行对比分析,结果表明,本文算法具有极高的实用性和安全性。结论本文算法完善了密钥冗余的问题,提高了算法的可行性,同时通过实验验证了算法的安全性,适合用于对各种尺寸的图像进行加密及相关的信息安全保障。
基金supported by the Science Foundation of State Ethnic Affairs Commission of the People's Republic of China(12ZNZ004)
文摘In this article, an elliptic system is investigated, which involves Hardy-type potentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argument, the Palais-Smale sequences of related approximation problems is analyzed and the existence of infinitely many solutions to the system is established.
基金Supported by National Natural Science Foundation of China(Grant No.10871090)
文摘In this paper, we study the planar Hamiltonian systemwhere where f is real analytic in x and θ,A（θ） is a 2×2real analytic symmetric matrix,J=（1^-1） and w is a Diophantine vector. Under the assumption that the unperturbed systemreducible and stable, we obtain a series of criteria for the stability and instability of the equilibrium of the perturbed system.
基金supported by National Natural Science Foundation of China (Grant No.11931012)the Fundamental Research Funds for the Central Universities (Grant No.CCNU22LJ002)Excellent Doctoral Dissertation Program at Central China Normal University in China (Grant No.2020YBZZ055)。
文摘This paper is concerned with ground states of two-component trapped Bose-Einstein condensates passing an obstacle in R^(2),where the intraspecies interactions are attractive and the interspecies interactions are repulsive.We address the classification on the existence and non-existence of ground states.The limiting profiles of ground states are also studied by the energy analysis and the elliptic partial differential equation theory.
文摘In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system {Sk1（λ（D2u1））＋a1（｜x｜）｜△u1｜k1=p1（｜x｜）f1（u2） for x∈RN,Sk2（λ（D2u2））＋a2（｜x｜）｜△u2｜k2=p2（｜x｜）f2（u1） for x∈RN.Here Ski （λ （D2ui）） is the ki-Hessian operator, a1, p1, f1, a2, p2 and f2 are continuous functions.
文摘The singularly perturbed problems for elliptic systems are considered. Undersuitable conditions, using the comparison theorem the asymptotic behavior of solution forthe boundary value problems are studied.
文摘This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.
