Abstract
This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.
Highlights
In this paper, we consider the uniqueness and existence of the positive solution for the following third-order differential equation u′′′(t ) + f (t,u (t )) = 0, t ∈ (0,1), (1)or u′′′(t ) + g (t,u (t ),u′(t )) = 0, t ∈ (0,1), (2)with the following three-point boundary conditions u= (0) u= ′(0) 0, u= ′(1) au′(η ) . (3)Throughout this paper, we assume that η ∈ (0,1), a ∈ (0,1 η ), f ∈ C ((0,1)×[0, ∞),[0, ∞)) may be singularHow to cite this paper: Hu, T.C. and Sun, Y.P. (2014) Existence and Uniqueness of Positive Solution for Third-Order ThreePoint Boundary Value Problems
Motivated mainly by the papers mentioned above, in this paper we will consider the uniqueness of the positive solution, the iteration and the rate of the convergence by the iteration for the nonlinear singular third-order three-point BVP (1)-(3)
We study the existence of the positive solution for the nonlinear third-order three-point BVP (2)-(3) by using the Leray-Schauder fixed point theorem
Summary
We consider the uniqueness and existence of the positive solution for the following third-order differential equation u′′′(t ) + f (t,u (t )) = 0, t ∈ (0,1),. (2014) Existence and Uniqueness of Positive Solution for Third-Order ThreePoint Boundary Value Problems. In the past few years, because of the extensive applications in mechanics and engineering, the existence of solutions or positive solutions for nonlinear singular or nonsingular three-point boundary value problems for third-order ordinary differential equations has been studied extensively in the literature (see [1]-[13] and references therein). Motivated mainly by the papers mentioned above, in this paper we will consider the uniqueness of the positive solution, the iteration and the rate of the convergence by the iteration for the nonlinear singular third-order three-point BVP (1)-(3).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
