Solvability of a quasilinear elliptic resonance equation on the N-torus

Abstract

In this article, we apply Galerkin-type techniques and Brouwer's fixed point theorem to obtain existence theorems of weak solutions for a quasilinear elliptic resonance equation Q(u)+f(x,u)=G on the N-torus in which the Landesman-Lazer condition for G may be excluded, the null space of Q may not be only constant functions, and the nonlinearity ƒ may grow superlinearly in u as|u|→∞.

Keywords:

• Galerkin-type technique
• Landesman-lazer condition

AMS Subject Classification:

• 35560
• 47H10