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In this paper, we discuss the existence of solutions for nonlinear q-difference equations with nonlocal q-integral boundary conditions. The first part of the paper deals with some existence and uniqueness results obtained by means of standard tools of fixed point theory. In the second part, sufficient conditions for the existence of extremal solutions for the given problem are established. The results are well illustrated with the aid of examples.

ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS