On positive solutions of a nonlinear equilibrium boundary value problem

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

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, ...

Positive Solutions of a Nonlinear Higher Order Boundary-value Problem

The authors consider the higher order boundary-value problem u(t) = q(t)f(u(t)), 0 ≤ t ≤ 1, u(i−1)(0) = u(n−2)(p) = u(n−1)(1) = 0, 1 ≤ i ≤ n− 2, where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.

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.