一类含Hardy位势的椭圆方程解的存在性

J4 ›› 2013, Vol. 48 ›› Issue (2): 62-66.

一类含Hardy位势的椭圆方程解的存在性

程永宽,姚仰新,韩亚蝶

华南理工大学数学系, 广东广州 510640

收稿日期:2012-04-09 出版日期:2013-02-20 发布日期:2013-03-04
作者简介:程永宽(1976- )，男，讲师，研究方向为动力系统与非线性椭圆型方程. Email: chengyk@scut.edu.cn
基金资助:
国家自然科学基金资助项目(10771074)

The existence of solutions for a elliptic equations with Hardy potential

CHENG Yong-kuang, YAO Yang-xin, HAN Ya-die

Department of Mathematics,South China University of Technology, Guangzhou 510640, Guangdong, China

Received:2012-04-09 Online:2013-02-20 Published:2013-03-04

摘要/Abstract

摘要：

建立一个新的Hilbert空间H, 在新的空间中讨论含Hardy位势的非线性椭圆方程,利用山路引理和(PS)条件, 证明方程非平凡解的存在性,再利用喷泉定理证明方程多重解的存在性。

关键词: 椭圆方程;Hardy位势;山路引理;喷泉定理

Abstract:

We establish a new Hilbert space and the existence of nontrivial solutions of nonlinear elliptic equation with Hardy potential and critical potential in the new Hilbert space by using the Mountain pass theorem with (PS) condition. Also, the existence of multiple solutions are proved by using Fountain theorem.

Key words: elliptic equation; Hardy potential; Mountain Pass lemma; Fountain theorem

程永宽,姚仰新,韩亚蝶. 一类含Hardy位势的椭圆方程解的存在性[J]. J4, 2013, 48(2): 62-66.

CHENG Yong-kuang, YAO Yang-xin, HAN Ya-die. The existence of solutions for a elliptic equations with Hardy potential[J]. J4, 2013, 48(2): 62-66.

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