Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type - Smirnov, Sergey (Nonlinear Analysis: Modelling and Control, 2021)
The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.
Keywords: third-order nonlinear boundary value problems; integral boundary conditions; existence and uniqueness of solutions; Green’s function; Banach fixed point theorem; Rus’s fixed point theorem