Solutions for a nonlinear fractional boundary value problem with sign-changing Greens function

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

This paper considers the existence, uniqueness and non-existence of solution for a quasi-linear fractional boundary value problems with sign-changing Green’s function. Under certain growth conditions on the nonlinear term, we employ the Leray-Schauder alternative fixed point theorem to obtain an existence result of nontrivial solution and use the Banach contraction mapping principle to obtain a...

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 a Fractional Boundary Value Problem with Changing Sign Nonlinearity

and Applied Analysis 3 A2 there exist g x , h x , and k t 0, such that 0 ≤ f t, x ≤ k t g x h x , ∀x ∈ 0,∞ , a.e. t ∈ 0, 1 , 1.6 here g : 0,∞ → 0,∞ is continuous and nonincreasing, h : 0,∞ → 0,∞ is continuous, and h/g is nondecreasing; A3 There exist two positive constants R > r > 0 such that R > ΦR1 γ∗ ≥ r > 0, ∫1 0 k s g ( rsα−1 ) ds < ∞, R ≥ ( 1 h R g R )∫1 0 1 − s α−β−1 Γ α ( 1 − aξα−β−1 s ...

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, ...