摘要：In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation { D q 2 u ( t ) = f ( t , u ( t ) , D q u ( t ) ) , t ∈ I , D q u ( 0 ) = 0 , D q u ( 1 ) = α u ( 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 D q u ( t ) in the equation.
关键词：q -difference equations ; Leray-Schauder nonlinear alternative ; boundary value problem ; fixed point theorem
