Singularly perturbed nonlinear Neumann problems under the conditions of Berestycki and Lions

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Let Omega be a bounded domain in R-N with the boundary partial derivative Omega is an element of C-3. We consider the following singularly perturbed nonlinear elliptic problem on Omega, epsilon(2)Delta nu - v + f(v)=0, v > 0 on Omega, partial derivative v/partial derivative nu = 0 on partial derivative Omega, where nu is the exterior normal to partial derivative Omega and the nonlinearity f is of subcritical growth. It has been known that under Berestycki and Lions conditions for f is an element of C-1(R) and N >= 3, there exists a solution nu(epsilon) of the problem which develops a spike layer near a local maximum point of the mean curvature H on partial derivative Omega for small epsilon > 0. In this paper, we extend the previous result for f is an element of C-0(R) and N >= 2. (C) 2011 Published by Elsevier Inc.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2012-03
Language
English
Article Type
Article
Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.252, no.6, pp.3848 - 3872

ISSN
0022-0396
DOI
10.1016/j.jde.2011.12.013
URI
http://hdl.handle.net/10203/103307
Appears in Collection
MA-Journal Papers(저널논문)
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