Multiple solutions for a nonlinear and non-homogeneous problem in   Orlicz-Sobolev spaces
  We study a non-homogeneous boundary value problem in a smooth bounded domain in $\mathbb{R}^N$. We prove the existence of at least two nonnegative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma. 
Mihai Mih\u{a}ilescu, Du\v{s}an Repov\v{s}
math.AP math.FA