Singularly perturbed nonlinear Neumann problems with a general nonlinearity
SCIE
SCOPUS
- Title
- Singularly perturbed nonlinear Neumann problems with a general nonlinearity
- Authors
- Byeon, J
- Date Issued
- 2008-05-15
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Abstract
- Let Omega be a bounded domain in R-n, n >= 3, 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 u - u + f(u) = 0, u > 0 on Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where v is an exterior normal to partial derivative Omega and a nonlinearity f of subcritical growth. Under rather strong conditions on f, it has been known that for small epsilon > 0, there exists a solution u(epsilon) of the above problem which exhibits a spike layer near local maximum points of the mean curvature H on partial derivative Omega as epsilon -> 0. In this paper, we obtain the same result under some conditions on f (Berestycki-Lions conditions), which we believe to be almost optimal. (C) 2008 Elsevier Inc. All rights reserved.
- Keywords
- LEAST-ENERGY SOLUTIONS; MULTIPEAK SOLUTIONS; ELLIPTIC PROBLEMS; EQUATIONS; EXISTENCE; PRINCIPLE; SYSTEM
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29363
- DOI
- 10.1016/J.JDE.2008.0
- ISSN
- 0022-0396
- Article Type
- Article
- Citation
- JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 244, no. 10, page. 2473 - 2497, 2008-05-15
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