BANACH FIXED POINT THEOREM IN APPLICATION TO NONLINEAR ELLIPTIC SYSTEMS - Afrouzi, G.A.; Zhang, Q.; Naghizadeh, Z. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
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 $H=H_0^1(Ω)× H_0^1(Ω)$ by applying the Banach fixed point theorem.