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Branches of solutions to semilinear biharmonic equations on RN

Published online by Cambridge University Press:  12 July 2007

Yinbin Deng  and
Yi Li
Yinbin Deng
Affiliation:
Department of Mathematics, Huazhong Normal University, Wuhan 430079, People's Republic of China (ybdeng@public.wh.hb.cn)
Yi Li
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha 410081, Hunan, People's Republic of China, and Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA (yi-li@uiowa.edu)
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Abstract

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For a large class of functions f, we consider the nonlinear biharmonic eigenvalue problem We describe the behaviour of the branch of solutions emanating from an eigenvalue of odd multiplicity below the essential spectrum of the linearized problem. The discussion is based on the degree theory for C2 proper Fredholm maps developed by Fitzpatrick, Pejsachowicz and Rabier.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 4 , August 2006 , pp. 733 - 758
Copyright
Copyright © Royal Society of Edinburgh 2006