Three-point boundary value problems of nonlinear second-order \(q\)-difference equations involving different numbers of \(q\). (English) Zbl 1397.39008

Sitthiwirattham, Thanin; Tariboon, Jessada; Ntouyas, Sotiris K.

J. Appl. Math. 2013, Article ID 763786, 12 p. (2013).

Summary: 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.

MSC:

39A13

Difference equations, scaling (\(q\)-differences)