Artículos de revistas
Concentrating standing waves for the fractional nonlinear Schrodinger equation
Journal of Differential Equations Volume 256, Issue 2, 15 January 2014, Pages 858–892
Dávila Bonczos, Juan
Pino Manresa, Manuel del
We consider the semilinear equation epsilon(2s)(-Delta)(s)u + V(x)u - u(p) = 0, u > 0, u is an element of H-2s(R-N) where 0 < s < 1, 1 < p < N+2s/N-2s, V (x) is a sufficiently smooth potential with inf(R) V(x) > 0, and epsilon > 0 is a small number. Letting w(lambda) be the radial ground state of (-Delta)(s) w(lambda) + lambda w(lambda) - w(lambda)(p) = 0 in H-2s (R-N), we build solutions of the form u epsilon(x) similar to (k)Sigma(i=1)w lambda(i)((x - xi(epsilon)(i))/epsilon), where lambda(i) = V(xi(epsilon)(i)) and the xi(epsilon)(i) approach suitable critical points of V. Via a Lyapunov-Schmidt variational reduction, we recover various existence results already known for the case s = 1. In particular such a solution exists around k nondegenerate critical points of V. For s = 1 this corresponds to the classical results by Floer and Weinstein  and Oh [24,25]. (C) 2013 Elsevier Inc. All rights reserved.