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 Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities Zhang, Jing1,2; Li, Shujie2,3; Wang, Yuwen2; Xue, Xiaoping1 2010-11-15 Source Publication JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS ISSN 0022-247X Volume 371Issue:2Pages:682-690 Abstract We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (I(t)), l > 2 and (II(t)), l >= 1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method. Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions. (C) 2010 Elsevier Inc. All rights reserved. Keyword Semilinear elliptic equations Neumann boundary condition Multiple solutions Jumping nonlinearity Fucik spectrum Degree theory Morse theory DOI 10.1016/j.jmaa.2010.05.045 Language 英语 Funding Project NSFC[10671049] ; NSFC[YJSCX 2008-157 HLJ] ; NSFC[10471098] ; NSFC[10671195] WOS Research Area Mathematics WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000280566900028 Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/10722 Collection 中国科学院数学与系统科学研究院 Corresponding Author Zhang, Jing Affiliation 1.Harbin Inst Technol, Dept Math, Harbin, Peoples R China2.Yuan Yung Tseng Funct Anal Res Ctr, Harbin 150025, Peoples R China3.Acad Sinica, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China Recommended CitationGB/T 7714 Zhang, Jing,Li, Shujie,Wang, Yuwen,et al. Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2010,371(2):682-690. APA Zhang, Jing,Li, Shujie,Wang, Yuwen,&Xue, Xiaoping.(2010).Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,371(2),682-690. MLA Zhang, Jing,et al."Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 371.2(2010):682-690.
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