The Existence and Multiplicity of Positive Solutions for a Third-order Three-point Boundary Value Problem

Abstract

The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone. Keywords Third-order ordinary differential equation, three-point boundary value problem, existence of n positive solutions, fixed point theorem on cone.

Positive solutions of nonlinear singular third-order two-point boundary value problem

“…Third order equations arise in a variety of different areas of applied mathematics and physics, as the deflection of a curved beam having a constant or varying cross section, three layer beam, electromagnetic waves or gravity driven flows and so on [13]. Different type of techniques have been used to study such problems: reduce them to first and/or second order equations [8]; use Green's functions and comparison principles [5,6,19] (for periodic boundary value conditions), [20][21][22][23][24][25] (three point boundary conditions), and [7,9,10,15,27] (two point ones).…”

Multiple positive solutions for nonlinear third order general three-point boundary value problems

“…Today, the boundary value problems (BVPs) play a major role in many fields of engineering design and manufacturing. Major established industries such as the automobile, aerospace, chemical, pharmaceutical, petroleum, electronics, and communications, as well as emerging technologies such as nanotechnology and biotechnology rely on the BVPs to simulate complex phenomena at different scales for design and manufactures of high-technology products; see, for example [9,17,18,19]. In these applied settings, positive solutions are meaningful.…”

Existence of triple positive solutions for a third-order three-point boundary value problem

“…For other existence results for third-order three-point BVP, one may see [2][3][4][8][9][10][12][13][14][15][16]18,19] and the references therein.…”