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In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {D 2 qu(t) = f (t, u(t),Dqu(t)), t ε I, D qu(0) = 0, Dqu(1) = αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains Dqu(t) in the equation. © 2013 Yu and Wang; licensee Springer.

Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives