Multiple positive solutions for nonlinear fractional q-difference equation with p-Laplacian operator

In this paper, we investigate a class of four-point boundary value problems of fractional q-difference equation with p-Laplacian operator which is the first time to be studied and is extended from a bending elastic beam equation. By Avery-Peterson theorem and the method of lower and upper solutions associated with monotone iterative technique, we obtain some sufficient conditions for the existence of multiple positive solutions. As applications, examples are presented to illustrate the main results.