数学物理学报 ›› 2015, Vol. 35 ›› Issue (3): 578-586.

• 论文 • 上一篇    下一篇

一类带负位势函数的超线性p-Laplace方程基态解的存在性

邓义华, 罗李平, 周立君   

  1. 衡阳师范学院数学与计算科学系 湖南 衡阳 421002
  • 收稿日期:2014-04-04 修回日期:2014-09-21 出版日期:2015-06-25 发布日期:2015-06-25
  • 作者简介:邓义华, dengchen4032@126.com
  • 基金资助:

    湖南省自然科学基金(14JJ2120)、湖南省教育厅重点项目(14A020)和湖南省重点建设学科([2011]76)资助

Existence of A Ground State Solution for A Class of Superlinear p-Laplace Equations with Negative Potential Functions

Deng Yihua, Luo Liping, Zhou Lijun   

  1. Department of Mathematical and Computational Sciences, Hengyang Normal University, Hunan Hengyang 421002
  • Received:2014-04-04 Revised:2014-09-21 Online:2015-06-25 Published:2015-06-25

摘要:

在没有Ambrosetti-Rabinowitz条件的情况下, 运用(C)c序列和变分方法讨论了p-Laplace方程基态解的存在性. 通过选择合适的Banach空间, 证明了RN上一类带负位势函数的超线性p-Laplace方程基态解的存在性.

关键词: 超线性p-Laplace方程, 基态解, (C)c序列, 变分方法

Abstract:

Using (C)c sequences and variational methods, we discuss the existence of a ground state solution to p-Laplace equations without the Ambrosetti-Rabinowitz condition. By chosing suitable Banach space, we prove that there exists a ground state solution to a class of superlinear p-Laplace equations with negative potential functions in RN.

Key words: Superlinear p-Laplace equations, Ground state solution, (C)c sequence, Varia-tional methods

中图分类号: 

  • O175.25