Existence of solutions of elliptic boundary value problems with mixed type nonlinearities

doi:10.1186/1687-2770-2012-97

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	Existence of solutions of elliptic boundary value problems with mixed type nonlinearities
	Mao,Anmin; Zhu,Yan; Luan,Shixia
	2012-08-31
发表期刊	Boundary Value Problems
ISSN	1687-2770
卷号	2012 期号:1
摘要	AbstractWe study the existence of a nontrivial solution of the following elliptic boundary value problem with mixed type nonlinearities:{?△u=f(x,u)in?Ω,u=0on??Ω,where f(x,u)=?Ku+Wu. We consider the problem in a different case: lim\|u\|→∞f(x,u)/u=∞, lim\|u\|→0f(x,u)/u is some constant. Assuming that K satisfies the “pinching” condition, and W satisfies a more general superquadratic growth condition than the well-known Ambrosetti-Rabinowitz condition usually used in literature, we obtain a nontrivial solution via the Mountain Pass Lemma.MSC:35J65, 35J20, 47J10.
关键词	pinching condition Mountain Pass Lemma Cerami condition
DOI	10.1186/1687-2770-2012-97
语种	英语
WOS记录号	BMC:10.1186/1687-2770-2012-97
出版者	Springer International Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/297
专题	中国科学院数学与系统科学研究院
通讯作者	Mao,Anmin
作者单位	Qufu Normal University; School of Mathematical Sciences
推荐引用方式 GB/T 7714	Mao,Anmin,Zhu,Yan,Luan,Shixia. Existence of solutions of elliptic boundary value problems with mixed type nonlinearities[J]. Boundary Value Problems,2012,2012(1).
APA	Mao,Anmin,Zhu,Yan,&Luan,Shixia.(2012).Existence of solutions of elliptic boundary value problems with mixed type nonlinearities.Boundary Value Problems,2012(1).
MLA	Mao,Anmin,et al."Existence of solutions of elliptic boundary value problems with mixed type nonlinearities".Boundary Value Problems 2012.1(2012).