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. 
Edcarlos D. Silva, Jose V. A. Goncalves, Kaye O. Silva
math.AP