Nontrivial Solutions for a Boundary Value Problem of nth-Order Impulsive Differential Equation

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.

Solutions to a boundary value problem of a fourth-order impulsive differential equation

This paper is concerned with the existence of solutions to a boundary value problem of a fourth-order impulsive differential equation with a control parameter λ. By employing some existing critical point theorems, we find the range of the control parameter in which the boundary value problem admits at least one solution. It is also shown that under certain conditions there exists an interval of...

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

Nontrivial Solutions for Boundary Value Problems of Nonlinear Differential Equation

The nonlinear three-point boundary value problem { −u′′(t) = f(t, u(t)), t ∈ I, βu(0)− γu′(0) = 0, u(1) = αu(η), is discussed under some conditions concerning the first eigenvalue corresponding to a special linear operator, where I = [0, 1], η ∈ (0, 1), α, β, γ ∈ [0,∞) with β + γ 6= 0, f : [0, 1] × (−∞,+∞) → (−∞,+∞) is sign–changing continuous function and may be unbounded from below. By applyi...

Positive Solutions of nth-Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary Conditions

Academic Editor: Feliz Manuel Minhós Copyright q 2011 Meiqiang Feng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper is devoted to study the existence, nonexistence, and multiplicity of positive solutions for the ...