TITLE:
Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem
AUTHORS:
Xiaoming Liu, Yongxiang Li
KEYWORDS:
Fully Third-Order BVP, Solution, Positive Solution, Existence and Uniqueness, Inequality Conditions
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.8,
August
14,
2023
ABSTRACT: The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.