Mountain pass solutions for singularly perturbed nonlinear Dirichlet problems
SCIE
SCOPUS
- Title
- Mountain pass solutions for singularly perturbed nonlinear Dirichlet problems
- Authors
- Byeon, HY
- Date Issued
- 2005-10-15
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Abstract
- We consider the following singularly perturbed nonlinear elliptic problem epsilon(2)Delta u - u + f(u) = 0, u > 0 in Omega, u = 0 on partial derivative Omega where the nonlinearity f is of subcritical growth and Omega is a bounded domain in R-n. Under certain conditions of f, there exists a mountain pass solution us for above problem and the solution u(epsilon) exhibits a spike layer as epsilon -> 0. To see the location of the spike layer for small epsilon > 0, some additional assumptions, certain nondegeneracy for a limiting problem or monotonicity of f(t)/t, have been assumed. In this paper, we characterize the location of the spike layer without such additional assumptions for n >= 3. (c) 2005 Elsevier Inc. All rights reserved.
- Keywords
- SCALAR FIELD-EQUATIONS; LEAST ENERGY SOLUTIONS; ELLIPTIC PROBLEMS; EXISTENCE
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29675
- DOI
- 10.1016/j.jde.2005.07.008
- ISSN
- 0022-0396
- Article Type
- Article
- Citation
- JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 217, no. 2, page. 257 - 281, 2005-10-15
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