Existence of Solutions To Second-Order Nonlinear Coupled Systems With Nonlinear Coupled Boundary Conditions

Abstract

In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations u ''(t) = f(t, v(t)), t is an element of[0,1], v '' (t) = g(t, u(t)), t is an element of [0, 1], with nonlinear coupled boundary conditions phi(u(0), v(0), u(1), v(1), u'(0), v'(0)) = (0, 0), psi(u(0), v(0), u(1),v(1),u'(1), v'(1)) = (0,0), where f, g: [0, 1] x R -> R and phi, psi : R-6 -> R-2 are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem. The results presented in this article extend those in [1, 3, 15].