Quasilinear elliptic systems of resonant type and nonlinear eigenvalue problems

Abstract

This work is devoted to the study of a quasilinear elliptic system of resonant type. We prove the existence of infinitely many solutions of a related nonlinear eigenvalue problem. Applying an abstract minimax theorem, we obtain a solution of the quasilinear system $-{\Delta }_{p}u=F_u\left(x,u,v\right),-{\Delta }_{q}v=F_v\left(x,u,v\right)$, under conditions involving the first and the second eigenvalues.