Resonance Problem of a Class of Quasilinear Parabolic Equations

In this paper, we study the resonance problem of a class of singular quasilinear parabolic equations with respect to its higher near-eigenvalues. Under a generalized Landesman-Lazer condition, it is proved that the resonance problem admits at least one nontrivial solution in weighted Sobolev spaces. The proof is based upon applying the Galerkin-type technique, the Brouwer s fixed-point theorem and a compact embedding theorem of weighted Sobolev spaces by Shapiro.