An existence result for a class of quasilinear elliptic boundary value problems with jumping nonlinearities

Abstract

We establish an existence result for a class of quasilinear elliptic boundary value problems with jumping nonlinearities using variational arguments. First we calculate certain homotopy groups of sublevel sets of the asymptotic part of the variational functional. Then we use these groups to show that the full functional admits a linking geometry and hence a min-max critical point.