Neumann边值问题变号解的存在性

Existence of sign-changing solutions with Neumann boundary value problem

利用下降流不变集方法并结合变分技巧,讨论在Neumann边界条件下二阶非线性差分方程的多解性与变号解,获得正解、负解以及变号解存在的充分条件.最后通过例子说明所得定理的有效性.

Making use of the method of invariant sets of descending flow in combination with variational method, we study the existence of multiple and sign-changing solutions for Neumann boundary value problem of a class of second-order nonlinear difference equations. Some sufficient conditions for the existence of positive solutions, negative solutions and sign-changing solutions are established. In addition, an example is given to verify the prac- tical effectiveness of our main theorem at length.