Solutions for a nonlinear fractional boundary value problem with sign-changing Green’s function

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, ...

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.

Existence and Uniqueness of Solutions for a Fractional Boundary Value Problem with Dirichlet Boundary Condition

The authors consider a nonlinear fractional boundary value problem with the Dirichlet boundary condition. An associated Green’s function is constructed as a series of functions by applying spectral theory. Criteria for the existence and uniqueness of solutions are obtained based on it.

Multiple Positive Solutions for a Third-order Three-point Bvp with Sign-changing Green’s Function

This article concerns the third-order three-point boundary-value problem u′′′(t) = f(t, u(t)), t ∈ [0, 1], u′(0) = u(1) = u′′(η) = 0. Although the corresponding Green’s function is sign-changing, we still obtain the existence of at least 2m−1 positive solutions for arbitrary positive integer m under suitable conditions on f .