Solvability of Third-Order Three-Point Boundary Value Problems with Carathéodory Nonlinearity (Communications in Mathematical Research, 2021)
A class of third-order three-point boundary value problems is considered,where the nonlinear term is a Carathéodory function. By introducing a height function and considering the integration of this height function, an existence theorem ofsolution is proved when the limit growth function exists. The main tools are theLebesgue dominated convergence theorem and the Schauder fixed point theorem.
Keywords: nonlinear ordinary differential equation; multi-point boundary value problem; existence.