Existence and multiplicity results for a degenerate quasilinear elliptic system near resonance

Abstract

Abstract We establish existence and multiplicity results for weak solutions of a degenerate quasilinear elliptic system. By using Ekeland’s variational principle, the mountain pass theorem and the saddle point theorem in critical point theory, we obtain the existence of one or three solutions for an elliptic system with Dirichlet boundary conditions under some restriction on λ . This kind of results was firstly obtained by Mawhin and Schmitt (Ann. Pol. Math. 51:241-248, 1990) for a semilinear two-point boundary value problem.