中文摘要：

在扰动项f1（x，u），f2（x，u）中，其中一项是超线性并且满足Ambrosetti—Rabinowitz条件，另一项为次线性的情形下，分别利用“喷泉定理”和“对偶喷泉定理”研究了无界区域RN上的p（x）-Laplace方程解的存在性和多解性问题．此问题是基于变指数Lebesgue和Sobolev空间进行讨论的．

英文摘要：

By using the fountain theorem and the dual fountain theorem, respectively, the existence and multiplicity of solutions for p（x）-Laplacian equations in Rg were studied, assumed that one of the perturbation terms f1 （x, u）, f2 （x, u） is superlinear and satisfies the Ambrosetti-Rabinowitz type condition and the other one is sublinear. The discussion was based on variable exponent Lebesgue and Sobolev spaces. Key words： variable exponent Sobolev spaces; p（x）-Laplacian; （PS）＊c condition; foun- tain theorem; dual fountain theorem