Existence of Solutions for a Class of Third-Order Ordinary Differential Equations Boundary Value Problems on an Infinite Interval

doi:10.13438/j.cnki.jdzk.2025.04.004

Abstract

Abstract: This paper investigates the existence of solutions for a class of third-order ordinary differential equation boundary value problems on an infinite interval.Firstly,the boundary value problems is equivalently transformed into the existence problems of fixed points for a class of integral operators in a suitable Banach space.Then,the complete continuity of the integral operators is proved by using the generalized Arzelá-Ascoli theorem.Finally,the Leray-Schauder principle are employed to establish an existence theorem of the solutions for this kind of boundary value problems.

Key words: third-order ordinary differential equations, boundary value problem on infinite intervals, Leray-Schauder principle, existence

SONG Guoxin, GOU Haide, LIU Jingfang. Existence of Solutions for a Class of Third-Order Ordinary Differential Equations Boundary Value Problems on an Infinite Interval[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(4): 19-27.

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