期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 244, 期 10, 页码 2473-2497出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2008.02.024
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- National Research Foundation of Korea [R01-2004-000-10055-0, 과06A1305] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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.
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