On some parametric elliptic systems at resonance

Abstract

In this paper, we study the resonance for some parametric elliptic systems in which the nonlinearities involve convection and convolution of the solution. By applying a topological method based on fixed point theory, we establish the existence of at least one weak solution without using Landesman–Lazer-type conditions. Furthermore, we deal with a gradient-type system at resonance and prove the existence of a solution by using a variational approach.