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

被引：3
|
作者：
Gao, Juanjuan [1 ,2 ]
Zhang, Yong [3 ]
Zhao, Peihao [1 ]
机构：
[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
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 381卷 / 01期
关键词：
Supercritical growth; Embedding theorem; Cylindrical domain; Mountain Pass Theorem; CRITICAL SOBOLEV EXPONENT; STAR-SHAPED DOMAINS; LOCAL MINIMIZERS; RADIAL SOLUTIONS; CONVEX NONLINEARITIES; NONTRIVIAL SOLUTIONS; ASYMPTOTIC-BEHAVIOR; CONTRACTILE DOMAINS; MULTIPLE SOLUTIONS; SMALL HOLES;
D O I：
10.1016/j.jmaa.2011.04.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：215 / 228
页数：14
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