一类临界位势非线性椭圆型方程非平凡解的存在性

J4 ›› 2013, Vol. 48 ›› Issue (4): 91-94.

一类临界位势非线性椭圆型方程非平凡解的存在性

伍芸1,2, 韩亚蝶1

1. 华南理工大学数学科学学院, 广东广州 510640; 2. 贵州师范大学数学与计算机科学学院, 贵州贵阳 550001

收稿日期:2010-05-15 出版日期:2013-04-20 发布日期:2013-04-16
作者简介:伍芸(1973- ),女,副教授,研究方向为非线性椭圆型方程.Email:wuyun73224@163.com
基金资助:
中央高校基础研究基金资助项目(D2116670);广东省自然科学基金资助项目(k3110090);贵州省科学技术厅—贵州师范大学联合基金(黔科合J字LKS［2012］14号)

Existence of nontrivial solutions of nonlinear elliptic equation with critical potential

WU Yun1,2, HAN Ya-die1

1. Department of Mathematics, South China University of Technology, Guangzhou 510640, Guangdong, China;
2. Department of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, Guizhou, China

Received:2010-05-15 Online:2013-04-20 Published:2013-04-16

摘要/Abstract

摘要：

建立了一个新的Hilbert空间H,在新的空间中讨论四维临界位势的非线性椭圆型方程,利用山路引理和(PS)条件,证明了方程非平凡解的存在性。

关键词: 非线性椭圆型方程;临界位势;非平凡解

Abstract:

Through the establishment of a new space H, the existence of nontrivial solutions of fourthorder nonlinear elliptic equation with critical potential in the new Hilbert space are discussed. It proves the existence problem of nontrivial solution in this new space by using the Mountain pass theorem and the (PS) condition.

Key words: nonlinear elliptic equation; critical potential; nontrivial solutions

伍芸1,2, 韩亚蝶1. 一类临界位势非线性椭圆型方程非平凡解的存在性[J]. J4, 2013, 48(4): 91-94.

WU Yun1,2, HAN Ya-die1. Existence of nontrivial solutions of nonlinear elliptic equation with critical potential[J]. J4, 2013, 48(4): 91-94.

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