Multiple nonsemitrivial solutions for quasilinear elliptic systems via associated eigenvalue problems

Abstract

In this paper, the existence, nonexistence and multiplicity of nonnegative solutions for quasilinear elliptic systems of resonant type involving $ (p,q) $-Laplacian are investigated. By using the generalized variant of the Nehari manifold and fibering method, we prove a suitable manifold with associated map for the systems and exploit the relation between them to study the existence and multiplicity of nonnegative solutions and obtain bifurcation results. Furthermore, we also apply the approach to treat a class of $ (p,q) $-Laplacian elliptic systems with concave-convex nonlinearities.