Existence and Location Results for Fully Nonlinear Boundary Value Problem of nth-Order Nonlinear System

Existence and Location Results for Fully Nonlinear Boundary Value Problem of nth-Order Nonlinear System

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.

The Existence of Countably Many Positive Solutions for Nonlinear nth-Order Three-Point Boundary Value Problems

We consider the existence of countably many positive solutions for nonlinear nth-order three-point boundary value problem u n t a t f u t 0, t ∈ 0, 1 , u 0 αu η , u′ 0 · · · u n−2 0 0, u 1 βu η , where n ≥ 2, α ≥ 0, β ≥ 0, 0 < η < 1, α β − α ηn−1 < 1, a t ∈ L 0, 1 for some p ≥ 1 and has countably many singularities in 0, 1/2 . The associated Green’s function for the nth-order three-point bounda...

Existence-Uniqueness Theorems for Three-Point Boundary Value Problems for nth-Order Nonlinear Differential Equations

where 01, ,l3, y and the x’s are real. It will be assumed throughout this paper that f (t, Ul , u, ,.-., un) is continuous on [CX, r] x R”. The approach taken here is similar to that of Barr and Sherman [I] and is based on the use of a solutionmatching technique that assumes existence and/or uniqueness of solutions to corresponding problems for the subintervals [cu, ,Kj and [p, y]. We refer to ...