一类非线性三阶微分方程边值问题解的存在唯一性

Abstract

The existence and uniqueness of solutions to the boundary value problem of a class of nonlinear 3rd-order differential equations were studied. Firstly, the results of the research on the boundary values of 3rd-order differential equations at home and abroad in recent years were combed. Then the boundary value problem of nonlinear 3rd-order differential equations with nonlinear boundary value conditions was put forth, and the solution to the related linear problem was explored. Finally, the Banach fixed point theorem was used to prove that the proposed boundary value problem has a unique solution. An example illustrates the applicability of the main results.