Nonhomogeneous Eigenvalue Problems with Singular and Critical Terms

Abstract

We consider a parametric Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which has singular and critical terms. Using cut-off techniques and variational methods, we show that for all small values of the parameter λ > 0, the problem has a positive solution and this solution converges to 0 in C_0^1(\overline{\Omega}) as λ to 0^+.