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论文类型：期刊论文

发表时间：2004-02-01

发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录刊物：Scopus、SCIE

卷号：290

期号：1

页面范围：21-34

ISSN号：0022-247X

关键字：elliptic boundary value problem; eigenvalue; Leray-Schauder principle

摘要：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.