On the solutions of the second-order $(p,q)$-difference equation with an application to the fixed-point theory

In this paper, we examined the existence and uniqueness of solutions to the second-order $(p,q)$-difference equation with non-local boundary conditions by using the Banach fixed-point theorem. Moreover, we introduced a special case of this equation called the Euler-Cauchy-like $(p,q)$-difference equation and provide its solution. We also studied the oscillation of solutions for this equation in $(p,q)$-calculus and proved the $(p,q)$-Sturm-type separation theorem and $(p,q)$-Kneser theorem about the oscillation of solutions.