Browsing by Author "Davila, Juan"

Now showing 1 - 5 of 5
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    Bistable Boundary Reactions in Two Dimensions
    (2011) Davila, Juan; del Pino, Manuel; Musso, Monica
    In a bounded domain Omega subset of R(2) with smooth boundary we consider the problem Delta U =0 in Omega, du/dv = i/epsilon f(u) on d Omega
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    Fast and slow decay solutions for supercritical elliptic problems in exterior domains
    (2008) Davila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng
    We consider the elliptic problem Delta u + u(p) = 0, u > 0 in an exterior domain, Omega = R(N)\D under zero Dirichlet and vanishing conditions, where D is smooth and bounded in R(N), N >= 3, and p is supercritical, namely p > N+2/N-2. We prove that this problem has infinitely many solutions with slow decay O(vertical bar x vertical bar(-2/p-1)) at infinity. In addition, a solution with fast decay O(vertical bar x vertical bar(2- N)) exists if p is close enough from above to the critical exponent.
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    Singular limits of a two-dimensional boundary value problem arising in corrosion modelling
    (2006) Davila, Juan; Del Pino, Manuel; Musso, Monica; Wei, Juncheng
    We consider the boundary value problem
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    Standing waves for supercritical nonlinear Schrodinger equations
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) Davila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng
    Let V (x) be a non-negative, bounded potential in R-N, N >= 3 and p supercritical, p > N+2/N-2. We look for positive solutions of the standing-wave nonlinear Schrodinger equation Delta u - V(x)u + u(P) = 0 in R-N, with u(x) -> 0 as vertical bar x vertical bar -> +infinity. We prove that if V(x) = 0(vertical bar x vertical bar(-2)) as vertical bar x vertical bar -> +infinity, then for N >= 4 and p > N+1/N-3 this problem admits a continuum of solutions. If in addition we have, for instance, V (x) = 0 (vertical bar x vertical bar-mu) with mu > N, then this result still holds provided that N >= 3 and p > N+2/N-2. Other conditions for solvability, involving behavior of V at infinity, are also provided. (C) 2007 Elsevier Inc. All rights reserved.
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    The supercritical Lane-Emden-Fowler equation in exterior domains
    (TAYLOR & FRANCIS INC, 2007) Davila, Juan; del Pino, Manuel; Muss, Monica
    We consider the exterior problem