Electron. J. Differential Equations, Vol. 2016 (2016), No. 309, pp. 1-13.

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

Fethi Soltani, Habib Yazidi

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.

Submitted April 26, 2016. Published November 30, 2016.
Math Subject Classifications: 35B45, 35P30, 35J65, 35J55.
Key Words: Biharmonic equation; non-variational system; a priori estimates.

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Fethi Soltani
Department of Mathematics
Faculty of Science
Jazan University , P.O. Box 277
Jazan 45142, Saudi Arabia
email: fethisoltani10@yahoo.com
Habib Yazidi
University of Tunis
National School of Engineering of Tunis
Depatment of Mathematics, 5 Street Taha Hssine
Bab Mnara 1008 Tunis, Tunisia
email: habib.yazidi@gmail.com

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