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Indexed by:期刊论文

Date of Publication:2004-02-01

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:Scopus、SCIE

Volume:290

Issue:1

Page Number:21-34

ISSN No.:0022-247X

Key Words:elliptic boundary value problem; eigenvalue; Leray-Schauder principle

Abstract:We investigate the existence of solutions of a nonlinear elliptic boundary value problem at resonance. Under the condition that the associated linear boundary value problem has no sign-changing solution or nontrivial solution and some other additional conditions, we prove the existence of solutions or nontrivial (even multiple) solutions to the nonlinear problem. Thus the existence of solutions can be obtained when the nonlinearity may cross any finite number of eigenvalues of the linear problem. (C) 2003 Elsevier Inc. All rights reserved.