Existence of solutions for a non-variational system of elliptic PDE's via topological methods

Abstract

In this article, we prove the existence of solutions for a non-variational system of elliptic PDE's. Also we study a system of bi-Laplacian equations with two nonlinearities and without variational assumptions. First, we prove a priori solution estimates, and then we use fixed point theory, to deduce the existence of solutions. Finally, to complement of the existence theorem, we establish a non-existence result.

Keywords

• Biharmonic equation
• non-variational system
• a priori estimates