Existence and uniqueness results for a third-order implicit differential equation

The purpose of this paper is to give sufficient conditions for the existence and uniqueness of solutions to the boundary value problem of a third-order implicit differential equation as follows: {f(t,u(t),u′(t),u‴(t))=0,0≤t≤1u(0)=u′(0)=u′(1)=0. The lower and upper solutions method, maximum principle together with an iterative technique are employed. An example illustrates the application of results obtained.