On the solvability of a quasilinear parabolic partial differential equation at resonance

In this article we apply Galerkin-type techniques and Brouwer’s fixed point theorem to obtain existence theorems of time-periodic solutions for quasilinear parabolic partial differential resonance equations of the Dirichlet boundary condition in which the Landesman–Lazer condition may be excluded.  2002 Elsevier Science (USA). All rights reserved