On Strongly Nonlinear Eigenvalue Problems in the Framework of Nonreflexive Orlicz-Sobolev Spaces

It is established existence and multiplicity of solutions for strongly nonlinear problems driven by the $Phi$-Laplacian operator on bounded domains. Our main results are stated without the so called $Delta_{2}$ condition at infinity which means that the underlying Orlicz-Sobolev spaces are not reflexive.