In this paper, we consider the existence of multiple solutions to the Kirchhoff problems with critical potential, critical exponent and a concave term. Our main tools are the Nehari manifold and mountain pass theorem.
In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component i...In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary, while the other is a Kirchhoff type wave equation with nonlinear memory.展开更多
In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the ...In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the bifurcation result,we determine the intervals ofλfor the existence,nonexistence,and exact multiplicity of one-sign solutions for this problem.展开更多
In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitabl...In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.展开更多
In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative tech...In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative technique.展开更多
In this paper, we establish the existence of at least four distinct solutions to an Kirchhoff type problems involving the critical Caffareli-Kohn-Niremberg exponent, concave term and sign-changing weights, by using th...In this paper, we establish the existence of at least four distinct solutions to an Kirchhoff type problems involving the critical Caffareli-Kohn-Niremberg exponent, concave term and sign-changing weights, by using the Nehari manifold and mountain pass theorem.展开更多
文摘In this paper, we consider the existence of multiple solutions to the Kirchhoff problems with critical potential, critical exponent and a concave term. Our main tools are the Nehari manifold and mountain pass theorem.
文摘In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary, while the other is a Kirchhoff type wave equation with nonlinear memory.
基金Supported by the National Natural Science Foundation of China(11561038)。
文摘In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the bifurcation result,we determine the intervals ofλfor the existence,nonexistence,and exact multiplicity of one-sign solutions for this problem.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(20110007870)
文摘In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.
文摘In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative technique.
文摘In this paper, we establish the existence of at least four distinct solutions to an Kirchhoff type problems involving the critical Caffareli-Kohn-Niremberg exponent, concave term and sign-changing weights, by using the Nehari manifold and mountain pass theorem.
