Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 196, Issue 2, Pages 211-264Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/S0022-1236(02)00013-7
Keywords
spike layer solutions; singular perturbation problems; semilinear elliptic equations; instability
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An abstract framework is given to establish the existence and compute the Morse index of spike layer solutions of singularly perturbed semilinear elliptic equations. A nonlinear Lyapunov-Schmidt scheme is used to reduce the problem to one on a normally hyperbolic manifold, and the related linearized problem is also analyzed using this reduction. As an application, we show the existence of a multi-peak spike layer solution with peaks on the boundary of the domain, and we also obtain precise estimates of the small eigenvalues of the operator obtained by linearizing at a spike layer solution. (C) 2002 Elsevier Science (USA). All rights reserved.
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