Existence of Three Positive Solutions for a Class of Boundary Value Problems of Caputo Fractional ｑ-Difference Equation

摘要

A class of boundary value problems of Caputo fractional ｑ-difference equation is introduced. Green’s function and its properties for this problem are deduced. By applying these properties and the Leggett-Williams fixed-point theorem, existence criteria of three positive solutions are obtained. At last, some examples are given to illustrate the validity of our main results.