One-Sided Resonance Problems for Quasilinear Elliptic Operators

We present some new existence results for a quasilinear elliptic problem with an unbounded driving force.The quasilinear elliptic operator is assumed to be variational and is such that 0 acts like an isolated eigenvalue with a corresponding eigenfunction which does not change sign.The driving force is further assumed to be in one-sided resonance around the eigenvalue 0, and a solvability condition of potential type is imposed.V ariational methods are used to obtain existence.Our results significantly improve earlier results of the authors.