Existence results for nonlinear two-parametric quantum difference
equation with first-order (p,q)-derivative
Abstract
In this paper, we study the solvability of a nonlinear two-parametric
quantum difference equation Dirichlet boundary value problem. At first,
we provide and prove the formula of changing the order of integration
for (p,q)-double integral. Second, We obtain the existence and
uniqueness criteria of solutions for this kind of boundary value problem
by using Banach contraction mapping principle, Leray-Schauder nonlinear
alternative theorem and Leray-Schauder continuation theorem. At last, we
give two examples to illustrate our results.