Existence and instability of spike layer solutions to singular perturbation problems
نویسندگان
چکیده
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. r 2002 Elsevier Science (USA). All rights reserved. MSC: 47H14; 35J25; 35P15; 46N20; 35B25
منابع مشابه
MR: Author Citations for Junping Shi
multiplicity of positive solutions for a class of semilinear problem. II. Junping Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability. multiplicity of positive solutions for a class of semilinear problems. Existence and instability of spike layer solutions to singular perturbation problems. J.
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تاریخ انتشار 2002