This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential w...This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential well V^-1(0).Combining this with other suitable assumptions on K and f,the existence of nontrivial solutions is obtained via variational methods.Furthermore,the concentration behavior of the nontrivial solution is also explored on the set V^-1(0)asλ→+∞as A—>H-oo as well.It is worth noting that the(PS)-condition can not be directly got as done in the literature,which makes the problem more complicated.To overcome this difficulty,we adopt different method.展开更多
In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity the...In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.展开更多
基金Supported by the Youth Foundation of Shangqiu Institute of Technology(2018XKQ01)。
文摘This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential well V^-1(0).Combining this with other suitable assumptions on K and f,the existence of nontrivial solutions is obtained via variational methods.Furthermore,the concentration behavior of the nontrivial solution is also explored on the set V^-1(0)asλ→+∞as A—>H-oo as well.It is worth noting that the(PS)-condition can not be directly got as done in the literature,which makes the problem more complicated.To overcome this difficulty,we adopt different method.
基金Supported by the Youth Foundation of Shangqiu Institute of Technology(No.2018XKQ01)
文摘In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.
