Coupled lower and upper solution approach for the existence of Solutions of nonlinear coupled system with nonlinear coupled boundary conditions

Abstract

The present article investigates the existence of Solutions of the following nonlinear second order coupled system with nonlinear coupled boundary conditions (CBCs) where f1,f2 : [0,1] x R → R, μ: R6 → R2 and υ : R2 →R2 arecontinuous functions. The results presented in [7, 11] are extended in our article. Coupled lower and upper solutions, Arzela-Ascoli theorem and Schauder’s fixed point theorem play an important role in estab-lishing the arguments. Some examples are taken to ensure the validity of the theoretical results.