Nonlinear hemivariational inequalities with eigenvalues near zero

@inproceedings{Gasinski2005NonlinearHI,
  title={Nonlinear hemivariational inequalities with eigenvalues near zero},
  author={Leszek Gasinski and Nikolaos S. Papageorgiou},
  year={2005}
}
In this paper we consider an eigenvalue problem for a quasilinear hemivariational inequality of the type $-\Delta_p x(z) -\lambda f(z,x(z))\in \partial j(z,x(z))$ with null boundary condition, where $f$ and $j$ satisfy ``$p-1$-growth condition''. We prove the existence of a nontrivial solution for $\lambda$ sufficiently close to zero. Our approach is variational and is based on the critical point theory for nonsmooth, locally Lipschitz functionals due to Chang [4].