Variational approach to bifurcation from infinity for nonlinear elliptic problems

Abstract

For any N ⩾ 1 and sufficiently small ε > 0, we find a positive solution of a nonlinear elliptic equationwhen lim|x| → ∞V(x) = m > 0 and some optimal conditions on f are satisfied. Furthermore, we investigate the asymptotic behaviour of the solution as ε → 0.