On radial solutions of inhomogeneous nonlinear scalar field equations

We study the existence of radially symmetric solutions u is an element of H(1)(Omega) of the following nonlinear scalar field equation -Delta u = g(vertical bar x vertical bar, u) in Omega. Here Omega = R(N) or {x is an element of R(N) vertical bar vertical bar x vertical bar > R}, N >= 2. We generalize the results of Li and Li (1993) [13] and Li (1990) [14] in which they studied the problem in R(N) and {vertical bar x vertical bar > R} with the Dirichlet boundary condition. Furthermore, we extend it to the Neumann boundary problem and we also consider the nonlinear Schrodinger equation that is the case g(r, s) = -V(r)s + (g) over tilde (s). (C) 2011 Elsevier Inc. All rights reserved.