Positive solutions of nonlinear three-point boundary-value problems

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Positive solutions of a nonlinear three-point boundary value problem

We study the existence of positive solutions to the boundary-value problem u + a(t)f(u) = 0, t ∈ (0, 1) u(0) = 0, αu(η) = u(1) , where 0 < η < 1 and 0 < α < 1/η. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.

Existence of Three Positive Solutions to Nonlinear Boundary Value Problems

Positive Solutions for Fourth-Order Three-Point Boundary-Value Problems

In this paper, we study sufficient conditions for the existence of at least three positive solutions for fourth-order three-point BVP.

Positive Solutions for Singular Three-point Boundary-value Problems

In this paper, we present the Green’s functions for a second-order linear differential equation with three-point boundary conditions. We give exact expressions of the solutions for the linear three-point boundary problems by the Green’s functions. As applications, we study uniqueness and iteration of the solutions for a nonlinear singular second-order three-point boundary value problem.