Recently the authors introduced in  the notions of qk-derivative and qk-integral of a function on finite intervals. As applications existence and uniqueness results for initial value problems for first and second order impulsive qk-difference equations was proved. In this paper, we study the existence and uniqueness of solutions for a boundary value problem of nonlinear second-order impulsive qk-difference equations with integral boundary conditions. Two results are obtained by applying Banach contraction principle and Leray-Schauder’s Nonlinear Alternative. Some examples are presented to illustrate the results.
Sudsutad, Weerawat; Tariboon, Jessada; and K. Ntouyas, Sotiris
"Existence of Solutions for Second-Order Impulsive q-Difference Equations with Integral Boundary Conditions,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 16.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss4/16