类p(x)-Laplace方程解的存在性

Existence of Solution for p(x)-Laplace Like Equation

应用变分法且以临界点理论为工具,利用山路引理,借助广义Lebesgue空间和广义Sobolev空间的基本理论,尤其是嵌入定理,H■lder不等式及Egorov定理获得了当非线性项满足超线性增长条件时,类p(x)-Laplace方程解的存在性.

In this paper, we use variational methods and Critical Point Theory as the main methods. By using mountain pass theorem, by means of the basic theory of generalized Lebesgue spaceLp(x)Ωand generalized Sobolev space W(m,p(x))(Ω), especially embedding theorem, H■derinequality and Egorov theorems, we study the existence of solution for p(x)-Laplace like equation, when nonlinearity owning a super-linear growth condition.