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Positive solution for a class of p-Laplacian fractional q-difference equations involving the integral boundary condition

Qi GE, Chengmin HOU

In this paper, we study the boundary value problem of a class of p-Laplacian fractional q-difference equations with parameter involving the integral boundary condition. The conditions for the existence of at least one positive solution is established together with the estimates of the lower and upper bounds of the solution at any instant of time. Our results are derived based on the method of upper and lower solutions and the Schauder fixed point theorem. As applications, an example is presented to illustrate our main results.