SINGULARLY PERTURBED NONLINEAR DIRICHLET PROBLEMS WITH A GENERAL NONLINEARITY

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Let Omega be a bounded domain in R(n), n >= 3, with a boundary partial derivative Omega is an element of C(2). We consider the following singularly perturbed nonlinear elliptic problem oil Omega: epsilon(2)Delta u - u + f(u) = 0, u > 0 on Omega, n = 0 on partial derivative Omega, where the nonlinearity f is of subcritical growth. Under rather strong conditions on f, it has been known that for small epsilon > 0, there exists a mountain pass solution u(epsilon) of above problem which exhibits a spike layer near a maximum point of the distance function d from partial derivative Omega as epsilon -> 0. In this paper, we construct a solution u(epsilon) of above problem which exhibits a spike layer near a maximum point of the distance function under certain conditions on f, which we believe to be almost optimal.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2010-04
Language
English
Article Type
Article
Citation

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.362, no.4, pp.1981 - 2001

ISSN
0002-9947
URI
http://hdl.handle.net/10203/103342
Appears in Collection
MA-Journal Papers(저널논문)
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