Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent
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Date
2006
Journal Title
Journal ISSN
Volume Title
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
We consider the boundary value problem Delta u + u(P) = 0 in a bounded, smooth domain Omega in R-2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Omega which ensure the existence of a positive solution up concentrating at exactly m points as p -> infinity. In particular, for a nonsimply connected domain such a solution exists for any given m >= 1. (c) 2006 Elsevier Inc. All rights reserved.
Description
Keywords
large exponent, concentrating solutions, Green's function, finite-dimensional reduction, CRITICAL SOBOLEV EXPONENT, VARIATIONAL PROBLEM, DIRICHLET PROBLEM, SINGULAR LIMITS, EQUATIONS, CONSTRUCTION, COMPACTNESS, EXISTENCE, DOMAINS