Spike solutions of a nonlinear Schrödinger equation with degenerate potential |
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Authors: | Sebastiá n Lorca |
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Affiliation: | a Universidad de Tarapacá, Departamento de Matemática, Casilla 7D, Arica, Chile b Universidade Estadual de Campinas, IMECC, Departamento de Matemática, Caixa Postal 6065, CEP 13083-970, Campinas, SP, Brazil |
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Abstract: | We study the existence of positive solutions to the elliptic equation ε2Δu(x,y)−V(y)u(x,y)+f(u(x,y))=0 for (x,y) in an unbounded domain subject to the boundary condition u=0 whenever is nonempty. Our potential V depends only on the y variable and is a bounded or unbounded domain which may coincide with . The positive parameter ε is tending to zero and our solutions uε concentrate along minimum points of the unbounded manifold of critical points of V. |
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Keywords: | Schrö dinger equation Degenerate potential Concentration |
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