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

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)
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