A Singular Third-order 3-point Boundary-value Problem with Nonpositive Green’s Function

Green’s function and positive solutions of a singular nth-order three-point boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a class of singular nth-order three-point boundary value problem. The associated Green’s function for the boundary value problem is given at first, and some useful properties of the Green’s function are obtained. The main tool is fixed-point index theory. The results obtained in this paper essentially improve and generalize s...

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.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...

A Third-order 3-point Bvp. Applying Krasnosel’skĭi’s Theorem on the Plane without a Green’s Function

Consider the three-point boundary value problem for the 3 order differential equation: