Landesman–Lazer type conditions for a system of p-Laplacian like operators

We study the existence of periodic solutions for a nonlinear second order system of ordinary differential equations of p-Laplacian type. Assuming suitable Nagumo and Landesman–Lazer type conditions we prove the existence of at least one solution applying topological degree methods.We extend a celebrated result by Nirenberg for resonant systems. © 2006 Elsevier Inc. All rights reserved.