On spikes concentrating on line-segments to a semilinear Neumann problem
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Date
2011
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ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
We consider the following singularly perturbed Neumann problem
-epsilon(2)Delta u + u - u(p) = 0 in Omega, u > 0 in Omega,
partial derivative u/partial derivative v = 0 on partial derivative Omega,
where p is subcritical and Omega is a smooth and bounded domain in R-n. We construct a new class of solutions which consist of large number of spikes concentrating on an interior straight-line intersecting with partial derivative Omega orthogonally. Our results show that higher-dimensional concentration can exist without resonance condition. (C) 2011 Elsevier Inc. All rights reserved.
-epsilon(2)Delta u + u - u(p) = 0 in Omega, u > 0 in Omega,
partial derivative u/partial derivative v = 0 on partial derivative Omega,
where p is subcritical and Omega is a smooth and bounded domain in R-n. We construct a new class of solutions which consist of large number of spikes concentrating on an interior straight-line intersecting with partial derivative Omega orthogonally. Our results show that higher-dimensional concentration can exist without resonance condition. (C) 2011 Elsevier Inc. All rights reserved.
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Keywords
INTERIOR PEAK SOLUTIONS, MULTIPEAK SOLUTIONS, LAYER SOLUTIONS, EXISTENCE, EQUILIBRIA, EQUATION, ENERGY