Orlicz-Sobolev 空间上对称及非对称拟线性椭圆方程的多解性

摘要

In this paper, we study multiplicity of solutions for the quasilinear elliptic prob-lem in a bounded domain with smooth boundary. By using variational and perturbed methods in Orlicz-Sobolev space, we prove the existence of multiple solutions both in symmetric and non-symmetric case.%本文研究了具光滑边界的有界域上拟线性椭圆问题的多解性。在Orlicz-Sobolev空间中利用变分及扰动的方法，得到了方程在对称及非对称情况下解的存在性和多解性。