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Orlicz-Sobolev空间上对称及非对称拟线性椭圆方程的多解性
杨阳¹, 张吉慧², 尚旭东³, 邵益新¹
1.江南大学理学院, 江苏无锡 214122;2.南京师范大学数学科学学院, 江苏南京 210046;3.南京师范大学泰州学院数科院, 江苏泰州 225300

摘要:

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.

关键词: Orlicz-Sobolev空间拟线性椭圆方程扰动方法对称性

DOI：

分类号:O175.25

基金项目:The first author is supported by NSFC-Tian Yuan Special Foundation (11226116);Natural Science Foundation of Jiangsu Province of China for Young Scholar (BK2012109);the China Scholarship Council (201208320435);the Fundamental Research Funds for the Central Universities (JUSRP11118);the second author is supported by NSFC (10871096);the third author is supported by Graduate Education Innovation of Jiangsu Province (CXZZ13-0389).

MULTIPLE SOLUTIONS FOR SYMMETRIC AND NON-SYMMETRIC QUASILINEAR ELLIPTIC EQUATIONS:AN ORLICZ-SOBOLEV SPACE SETTING

YANG Yang¹, ZHANG Ji-hui², SHANG Xu-dong³, SHAO Yi-xin¹

1.School of Science, Jiangnan University, Wuxi 214122, China;2.School of Mathematics Science, Nanjing Normal University, Nanjing 210046, China;3.School of Mathematics, Nanjing Normal University Taizhou College, Taizhou 225300, China

Abstract:

In this paper,we study multiplicity of solutions for the quasilinear elliptic problem 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 nonsymmetric case.

Key words: Orlicz-Sobolev spaces quasilinear elliptic equations perturbed methods symmetry