自然增长条件下含Hardy位势的椭圆型方程解的存在性

数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1470-1478.

自然增长条件下含Hardy位势的椭圆型方程解的存在性

李周欣¹|沈尧天²

1.北京大学数学科学学院北京 100871；2.华南理工大学数学科学学院广州 510640

收稿日期:2010-10-26 修回日期:2011-12-10 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
中国博士后科学基金资助

Existence of Solutions for Elliptic Equations Involving Hardy Potential under Natural Growth Condition

LI Zhou-Xin¹, SHEN Yao-Tian²

1.School of Mathematical Sciences, Peking University, Beijing 100871|2.School of Mathematical Sciences, South China University of Technology, Guangzhou 510640

Received:2010-10-26 Revised:2011-12-10 Online:2011-12-25 Published:2011-12-25
Supported by:
中国博士后科学基金资助

摘要/Abstract

摘要：

该文讨论自然增长条件下含Hardy位势的拟线性椭圆型方程解的存在性. 我们把通常利用到的符号条件减弱到小于零的情况,证明此时方程对应的能量泛函仍满足(PS)条件, 再利用不光滑泛函的临界点定理,证明方程存在着两个特性各异的非平凡解.

关键词: 椭圆型方程, 自然增长条件, Hardy位势, 不光滑临界点定理

Abstract:

In this paper, the authors study a quasilinear elliptic equation with Hardy potential under natural growth condition. The authors extend the sign condition from nonnegative to a minus part, prove that at this time the corresponding functional of the equation still satisfies the (PS) condition, and then prove the existence of two nontrivial weak solutions via the nonsmooth critical point theory.

Key words: Elliptic equation, Natural growth condition, Hardy potential, Nonsmooth critical point theory

中图分类号:

35J35

李周欣, 沈尧天. 自然增长条件下含Hardy位势的椭圆型方程解的存在性[J]. 数学物理学报, 2011, 31(6): 1470-1478.

LI Zhou-Xin, SHEN Yao-Tian. Existence of Solutions for Elliptic Equations Involving Hardy Potential under Natural Growth Condition[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1470-1478.

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