二阶耦合非线性差分系统边值问题

In this paper, we mainly discuss the existence of nontrivial solutions to the boundary value problems for a coupled nonlinear difference system. First, we establish a suitable variational functional and transfer the existence of solutions of the boundary value problems of the coupled nonlinear difference system into that of the critical points of the corresponding functional. A new critical point theorem is established by using the variant of the mountain pass theorem and the local minimum theorem. By using this critical point theorem, we obtain some conditions of the existence of nontrivial solutions, with neither of the components is identically zero, to the boundary value problems of the coupled nonlinear difference system.