Positive solutions for P-Laplace problems with nonlinear time-fractional differential equation

被引：1

作者：

Qiu, Meilan ^{[1
]}

Mei, Liquan ^{[1
]}

Yang, Ganshan ^{[2
,3
]}

Yuan, George Xianzhi ^{[4
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

[2] Yunnan Nationalities Univ, Dept Math, Kunming 650031, Peoples R China

[3] Yunnan Normal Univ, Inst Math, Kunming 650092, Peoples R China

[4] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2014年

基金：

中国国家自然科学基金;

关键词：

Nehari manifold; concave-convex nonlinearities; positive weight function; weighted Sobolev space; time-fractional equation; fixed point theorem; SEMILINEAR ELLIPTIC-EQUATIONS; PROBLEMS INVOLVING CONCAVE; FIXED-POINT THEOREMS; DIRICHLET PROBLEMS; CONVEX NONLINEARITIES;

D O I：

10.1186/1029-242X-2014-262

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the existence and multiplicity of positive solutions for semi-linear elliptic equations with a sign-changing weight function in weighted Sobolev spaces. By investigating the compact embedding theorem and based on the extraction of the Palais-Smale sequence in the Nehari manifold which is a subset of the weighted Sobolev spaces, we derive the existence of the multiple positive solutions of the equations by using the variational method. In the last part of this paper, by applying the Arzela-Ascoli fixed point theorem, some existence results of the corresponding time-fractional equations for semi-linear elliptic equations are obtained.

引用

页数：22