Title: Existence and multiplicity of positive solutions for fractional q-difference equations with parameter

Authors: Xinhui Li; Zhenlai Han; Yan Zhao

Addresses: School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China ' School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China ' School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Abstract: In this paper, we study the boundary value problem of a class of nonlinear fractional q-difference equations with multi-point boundary conditions with parameter involving the Riemann-Liouuville fractional q-derivative. By means of the Banach contraction mapping principle, Schauder fixed point theorem and Leggett-Williams fixed point theorem, some results of existence, uniqueness, nonexistence and multiple of positive solutions are obtained. At last, examples are presented to illustrate our main results.

Keywords: fractional q-difference equations; multi-point boundary conditions; parameters; boundary value problem; contraction mapping principle; fixed point theorems; positive solutions.

DOI: 10.1504/IJDSDE.2015.072838

International Journal of Dynamical Systems and Differential Equations, 2015 Vol.5 No.4, pp.267 - 287

Received: 22 Apr 2014
Accepted: 06 Dec 2014
Published online: 04 Nov 2015 *

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