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

DOI: http://dx.doi.org/10.12775/TMNA.2002.029

#### 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.

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.

#### Keywords

quasilinear elliptic boundary value problems; jumping nonlinearities; Fucik spectrum; critical point theory on $C^1$-Finsler manifolds; homotopy theory; linking; min-max principle

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