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Existence and multiplicity of positive solutions for nonhomogeneous boundary value problems with fractional q-derivatives

Yulin Zhao1*, Haibo Chen2 and Qiming Zhang1

Author Affiliations

1 School of Science, Hunan University of Technology, Zhuzhou, 412007, China

2 Department of Mathematics, Central South University, Changsha, 410075, China

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Boundary Value Problems 2013, 2013:103  doi:10.1186/1687-2770-2013-103

Published: 25 April 2013

Abstract

In this paper, we study a class of fractional q-difference equations with nonhomogeneous boundary conditions. By applying the classical tools from functional analysis, sufficient conditions for the existence of single and multiple positive solutions to the boundary value problem are obtained in term of the explicit intervals for the nonhomogeneous term. In addition, some examples to illustrate our results are given.

MSC: 34A08, 34B18, 39A13.

Keywords:
fractional q-difference equation; nonhomogeneous boundary value problem; positive solution; multiplicity