Abstract
In this paper, we are concerned with the following nonlinear third-order -point boundary value problem: , , , , . Some existence criteria of solution and positive solution are established by using the Schauder fixed point theorem. An example is also included to illustrate the importance of the results obtained.
Highlights
Third-order differential equations arise in a variety of different areas of applied mathematics and physics, for example, in the deflection of a curved beam having a constant or varying cross-section, a three-layer beam, electromagnetic waves, or gravity-driven flows and so on 1
Yao 10 employed the Leray-Schauder fixed point theorem to prove the existence of solution and positive solution for the BVP
Fixed Point Theory and Applications worth mentioning that Jin and Lu 12 studied some third-order differential equation with the following m-point boundary conditions: m−2 u 0 0, u 1 aiu ξi, u 0 0
Summary
Third-order differential equations arise in a variety of different areas of applied mathematics and physics, for example, in the deflection of a curved beam having a constant or varying cross-section, a three-layer beam, electromagnetic waves, or gravity-driven flows and so on 1.Recently, third-order two-point or three-point boundary value problems BVPs have received much attention from many authors; see 2–10 and the references therein. Yao 10 employed the Leray-Schauder fixed point theorem to prove the existence of solution and positive solution for the BVP The purpose of this paper is to consider the local properties of f on some bounded sets and establish some existence criteria of solution and positive solution for the BVP 1.3 by using the Schauder fixed point theorem.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
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 call