We study a new class of three-point boundary value problems of nonlinear second-order q-difference equations. Our problems contain different numbers of q in derivatives and integrals. By using a variety of fixed point theorems (such as Banach’s contraction principle, Boyd and Wong fixed point theorem for nonlinear contractions, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative) and Leray-Schauder degree theory, some new existence and uniqueness results are obtained. Illustrative examples are also presented.
"Three-Point Boundary Value Problems of Nonlinear Second-Order -Difference Equations Involving Different Numbers of ." J. Appl. Math. 2013 1 - 12, 2013. https://doi.org/10.1155/2013/763786