SINGULARLY PERTURBED NONLINEAR DIRICHLET PROBLEMS WITH A GENERAL NONLINEARITY
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SCOPUS
- Title
- SINGULARLY PERTURBED NONLINEAR DIRICHLET PROBLEMS WITH A GENERAL NONLINEARITY
- Authors
- Byeon, J
- Date Issued
- 2010-04
- Publisher
- AMER MATHEMATICAL SOC
- Abstract
- 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.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/12975
- DOI
- 10.1090/S0002-9947-09-04746-1
- ISSN
- 0002-9947
- Article Type
- Article
- Citation
- TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 362, no. 4, page. 1981 - 2001, 2010-04
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