Existence results for a coupled system of nonlinear fourth-order differential equations (Q2015366)

Summary: The purpose of this paper is to study the existence of solutions to the following coupled system of nonlinear fourth-order differential equations: \[ \begin{gathered} x''''(t)=f(t,x(t), \quad t\in (0,1),\\ x''''(t)=g(t,x(t), \quad t\in (0,1),\\ x(0)=x''(0)=0, \quad x'(1)=0,\\ x'''(1)=\xi(x(1)),\\ y(0)=y''(0)=0,\quad y'(1)=0,\\ y'''(1)=\zeta(y(1)), \end{gathered} \] where \(f,g:[0,1] \times\mathbb{R} \times \mathbb{R}\to\mathbb{R}\) and \(\xi,\zeta: \mathbb{R}\to\mathbb{R}\) are given continuous functions.