SPIKE LAYER SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM: VARIATIONAL CONSTRUCTION WITHOUT A NONDEGENERACY

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We consider the following singularly perturbed problem epsilon(2)Delta u - u + f(u) = 0, u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega. Existence of a solution with a spike layer near a min-max critical point of the mean curvature on the boundary partial derivative Omega is well known when a nondegeneracy for a limiting problem holds. In this paper, we use a variational method for the construction of such a solution which does not depend on the nondengeneracy for the limiting problem. By a purely variational approach, we construct the solution for an optimal class of nonlinearities f satisfying the Berestycki-Lions conditions.
Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
Issue Date
2019-07
Language
English
Article Type
Article
Citation

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.18, no.4, pp.1921 - 1965

ISSN
1534-0392
DOI
10.3934/cpaa.2019089
URI
http://hdl.handle.net/10203/250337
Appears in Collection
MA-Journal Papers(저널논문)
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