Browsing by Author "Davila, Juan"
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- ItemStanding waves for supercritical nonlinear Schrodinger equations(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) Davila, Juan; del Pino, Manuel; Musso, Monica; Wei, JunchengLet 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.
- ItemThe supercritical Lane-Emden-Fowler equation in exterior domains(TAYLOR & FRANCIS INC, 2007) Davila, Juan; del Pino, Manuel; Muss, MonicaWe consider the exterior problem