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1. Singularly perturbed nonlinear Neumann problems under the conditions of Berestycki and Lions

Author

Byeon, Jaeyoung and Lee, Youngae

Subjects
*NEUMANN problem, *MATHEMATICAL singularities, *PERTURBATION theory, *NONLINEAR theories, *CURVATURE, *PROBLEM solving
Abstract

Abstract: Let Ω be a bounded domain in with the boundary . We consider the following singularly perturbed nonlinear elliptic problem on Ω, where ν is the exterior normal to ∂Ω and the nonlinearity f is of subcritical growth. It has been known that under Berestycki and Lions conditions for and , there exists a solution of the problem which develops a spike layer near a local maximum point of the mean curvature H on ∂Ω for small . In this paper, we extend the previous result for and . [Copyright &y& Elsevier]

Published
2012
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