Existence of Solutions for Nabla-differentiable Systems of the Second Order

Abstract

We establish the existence of solutions to systems of second-order differential equations in time scales. The problem is of type nabla differential of order two with the member f being a $\nabla-$caratheodory function. We consider differential systems in which the nonlinearity f depends on the derivative nabla $u^{\nabla}$. The existence results are based on the notion of solution-tube and the fixed point theorem.