On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent

We consider the nonlinear eigenvalue problem \[ − div ( | ∇ u | p ( x ) − 2 ∇ u ) = λ | u | q ( x ) − 2 u -\textrm {div}\left (|\nabla u|^{p(x)-2}\nabla u\right )=\lambda |u|^{q(x)-2}u \] in Ω \Omega , u = 0 u=0 on ∂ Ω \partial \Omega , where Ω \Omega is a bounded open set in R N \mathbb R^N with sm... View More