Multiple Positive Solutions for a Nonlinear Three-Point Integral Boundary-Value Problem

Abstract

We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problemαη 2 −2η+2T are given constants. We establish the existence of at least three positive solutions by using the Leggett-Williams fixed-point theorem.2000 Mathematics Subject Classification. 34B15, 34C25, 34B18.

Solvability for a nonlinear third-order three-point boundary value problem

“…We quote also the reasearchs of [2,4,5,6,7,8,12,13,14,15,16,18,20] which concern the differential equations under various boundary conditions and by different approaches. Motivated by the works mentioned above, we obtain the existence results for the problem (1.1)-(1.2) by using the Leray-Shauder fixed point theorem if f 0 = 0 ( condition f ∞ = ∞ being unnecessary ) , as well as, for f ∞ = 0 ( condition f 0 = ∞ being unnecessary ).…”

Positive solutions of a nonlinear three-point eigenvalue problem with integral boundary conditions

“…In [9], by using Leggett-Williams fixed-point theorem, the authors considered the multiplicity of positive solutions of the following three-point integral boundary value problem (BVP)…”

Positive solutions of a nonlinear three-point boundary value problem with integral boundary conditions

“…In [9,10], the authors considered the following three-point integral boundary value problem (BVP) u ′′ (t) + a(t)f (u(t)) = 0, t ∈ (0, T ), (1.6)…”

“…Motivated by the results of [20,9,10] the aim of this paper is to establish some simple criterions for the existence of positive solutions of the BVP (1.1), (1.2). In Section 2, we prove several preliminary results that will be used to prove our results.…”