一类分数阶椭圆型方程解的存在性

吉林大学学报(理学版)

一类分数阶椭圆型方程解的存在性

关丽红¹, 常晶², 赵昕³

1. 长春大学理学院, 长春 130022; 2. 空军航空大学基础部, 长春 130022;3. 吉林农业大学信息技术学院, 长春 130118

收稿日期:2013-10-28 出版日期:2014-07-26 发布日期:2014-09-26
通讯作者: 关丽红 E-mail:zqd_cc@sina.com

Existence of Solutions for Some Elliptic Equations with Fractional

GUAN Lihong¹, CHANG Jing², ZHAO Xin³

1. College of Science, Changchun University, Changchun 130022, China;2. Department of Foundation, Aviation University of Air Force, Changchun 130022, China;3. College of Information Technology, Jilin Agricultural University, Changchun 130118, China

Received:2013-10-28 Online:2014-07-26 Published:2014-09-26
Contact: GUAN Lihong E-mail:zqd_cc@sina.com

摘要/Abstract

摘要：

考虑分数阶椭圆型方程(-Δ)su=f(x,u)在Dirichlet边界条件下非平凡解的存在性, 应用推广形式的山路定理得到了当非线性项满足渐近线性增长时, 该椭圆型方程非平凡解的存在性.

关键词: 分数阶Laplace方程, Dirichlet边值条件, 山路定理

Abstract:

This paper deals with the existence of solutions for some fractional elliptic equation (-Δ)su=f(x,u) under Dirichlet boundary condition. When the asymptotic growing of the nonlinearity f at zero and infinity was maintained, a new existence result was obtained by means of used the mountain pass theorem.

Key words: fractional Laplace equation, Dirichlet boundary condition, mountain pass theorem

中图分类号:

O175.25

关丽红, 常晶, 赵昕. 一类分数阶椭圆型方程解的存在性[J]. 吉林大学学报(理学版), 2014, 52(04): 737-739.

GUAN Lihong, CHANG Jing, ZHAO Xin. Existence of Solutions for Some Elliptic Equations with Fractional[J]. Journal of Jilin University Science Edition, 2014, 52(04): 737-739.

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