Abstract
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. Variational methods are used to obtain existence. Our results significantly improve earlier results of the authors.
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