Existence and uniqueness results for third-order nonlinear differential systems

Sufficient conditions are given for the existence of solutions to third order boundary value problems for nonlinear differential systems. Some appropriate conditions are given to guarantee that the Nagumo condition is satisfied. By constructing appropriate a lower solution-upper solution pair, a concept that is defined in this paper, the uniqueness result of the problem is also established. The emphasis here is that the differential systems has nonlinear dependence on all over order derivatives and the boundary conditions are nonlinear.