Variational approach to bifurcation from infinity for nonlinear elliptic problems

Abstract

For any N >= 1 and sufficiently small epsilon > 0, we find a positive solution of a nonlinear elliptic equation Delta u = epsilon(2)(V(x)u - f(u)), x is an element of R-N, when lim(vertical bar x vertical bar ->infinity) V(x) = m > 0 and some optimal conditions on f are satisfied. Furthermore, we investigate the asymptotic behaviour of the solution as epsilon -> 0.