Existence of positive solutions for a class of semilinear and quasilinear elliptic equations with supercritical case

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:381

Article

Gao, Juanjuan^1,2  Zhang, Yong³  Zhao, Peihao¹ 

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[2] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471003, Peoples R China

[3] Chizhou Univ, Dept Math & Comp Sci, Chizhou 247000, Peoples R China

关键词: Supercritical growth;    Embedding theorem;    Cylindrical domain;    Mountain Pass Theorem;   

DOI  :  10.1016/j.jmaa.2011.04.003

来源: Elsevier

【 摘 要 】

In this paper, we consider a class of semilinear elliptic Dirichlet problems in a bounded regular domain with cylindrical symmetry involving concave-convex nonlinearities with supercritical growth. Using a new Sobolev embedding theorem and variational method, we show the existence of two positive solutions of the problem. Additionally, we study the quasilinear elliptic equation and obtain a similar result. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free