一类二阶非线性差分方程Dirichlet边值问题的多解性和变号解

Sign-changing Solutions for A Class of Discrete Second-order Dirichlet Boundary Value Problem

应用下降流不变集理论和变分技巧,当参数满足适当的条件时,建立二阶非线性差分方程Dirichlet边值问题存在正解、负解和变号解的充分条件.最后通过一个例子说明定理结论的有效性.

Using invariant sets of descending flow and variational methods, when the parameter belongs to appropriate intervals, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinear difference equations with Dirichlet boundary value problem. Finally, an example is given to illustrate our results.