Positive solutions of nonlinear singular boundary value problem in abstract space

Multiple Positive Solutions for Nonlinear Singular Third-order Boundary Value Problem in Abstract Spaces

In this paper, we study the nonlinear singular boundary value problem in abstract spaces: { u′′′ + f(t, u) = θ, t ∈ (0, 1), u(0) = u′(0) = θ, u′(1) = ξu′(η), where 0 < η < 1 and 1 < ξ < 1 η , θ denotes the zero element of E, E is a real Banach space, and f(t, u) is allowed to be singular at both end point t = 0 and t = 1. We show the existence of at least two positive solutions of this problem.

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, ...

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

Positive solutions for nonlinear singular boundary value problems

We discuss the existence of positive solutions for singular secondorder boundary value problems x′′ = μf (t, x, x′), ax(0) − bx′(0) = k ≥ 0, x′(∞) = 0, where f may be singular at x = 0 and x′ = 0 and can change sign. Via fixed point theory, we establish the existence of positive solutions under some conditions on f . Our results deal with the situation where the solutions approach the singulari...