Existence of nonnegative solutions for a fractional m-point boundary value problem at resonance
نویسندگان
چکیده
منابع مشابه
On the existence of nonnegative solutions for a class of fractional boundary value problems
In this paper, we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation. By applying Kranoselskii`s fixed--point theorem in a cone, first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function. Then the Arzela--Ascoli theorem is used to take $C^1$ ...
متن کاملThe Existence of Solutions for a Nonlinear Fractional Multi-Point Boundary Value Problem at Resonance
Xiaoling Han and Ting Wang Department of Mathematics, Northwest Normal University, Lanzhou 730070, China Correspondence should be addressed to Xiaoling Han, [email protected] Received 16 May 2011; Accepted 16 June 2011 Academic Editor: Nikolai Leonenko Copyright q 2011 X. Han and T. Wang. This is an open access article distributed under the Creative Commons Attribution License, which perm...
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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.
متن کاملExistence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation
and Applied Analysis 3 Definition 2.2 see 18 . The standard Riemann-Liouville fractional derivative of order α > 0 of a continuous function y : a,∞ → R is given by D a y t 1 Γ n − α ( d dt )n ∫ t a t − s n−α−1y s ds, 2.2 where n α 1, provided that the integral on the right-hand side converges. Definition 2.3 see 18 . The Riemann-Liouville fractional integral of order α > 0 of a function y : a,∞...
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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, ...
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ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2013
ISSN: 1687-2770
DOI: 10.1186/1687-2770-2013-127