Upper and lower solutions method for a class of second-order coupled systems (Q6571648)

The authors consider a system of second order coupled ordinary differential equations with Dirichlet boundary conditions. They propose a method of upper and lower solution that provides an existence result. In the proof they utilize homotopy parameter method, degree theory and a maximum principle. Some examples of concerete second order systems are included. A special case of system under consideration arises from writing the nonlinear elastic beam equation in a form of a system of coupled second order equations.