BANACH FIXED POINT THEOREM IN APPLICATION TO NONLINEAR ELLIPTIC SYSTEMS

G.A.  Afrouzi; Q. Zhang; Z.  Naghizadeh

BANACH FIXED POINT THEOREM IN APPLICATION TO NONLINEAR ELLIPTIC SYSTEMS

Authors

G.A. Afrouzi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
Q. Zhang Department of Mathematics and Information Science,Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China
Z. Naghizadeh Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Keywords:

Weak solution, Nonlinear elliptic system, The Laplace operator, Banach fixed point theorem

Abstract

This paper is concerned with some nonlinear elliptic systems. Under suitable conditions on the nonlinearities $f$ and $g$, we obtain weak solution in Sobolev space $H=H_0^1(\Omega)\times H_0^1(\Omega)$ by applying the Banach fixed point theorem.