一类带有变指数增长的Neumann问题

A Class of Neumann Problems with Variable Exponential Growth

考虑一类带有变号位势和变指数的半线性Neumann边值问题,通过空间分解技术和变号位势函数的一些性质,证明了该类问题的泛函满足(PS)条件且具有山路几何结构,利用变分方法获得了该类问题两个非平凡解的存在性.

In this paper,we consider a class of semilinear Neumann boundary value problems with variable sign potential function and variable exponent.Using the space decomposition technique and some properties of sign-changing potential function,we prove that the functional of such problems satisfies the(PS)conditions and has astructure of mountain pass geometry.With the variational method,we obtain the existence of two nontrivial solutions of these problems.