Abstract
In this paper, we study boundary value problems for q-difference equa- tions and inclusions with nonlocal and integral boundary conditions. Some new exis- tence and uniqueness results are obtained by using a variety of xed point theorems. Examples are given to illustrate the results.
Highlights
The study of q-difference equations, initiated by Jackson [22, 23], Carmichael [11], Mason [27] and Adams [1] in the first quarter of 20th century, has been developed over the years, for instance, see [15, 17]
We study boundary value problems for q-difference equations and inclusions with nonlocal and integral boundary conditions
Some new existence and uniqueness results are obtained by using a variety of fixed point theorems
Summary
The study of q-difference equations, initiated by Jackson [22, 23], Carmichael [11], Mason [27] and Adams [1] in the first quarter of 20th century, has been developed over the years, for instance, see [15, 17]. There are many aspects of boundary value problems of q-difference equations that need attention. Ahmad and S.K. Ntouyas instance, q-difference equations with nonlocal and integral boundary conditions are yet to be addressed. In this paper, motivated by some recent theoretical work on the topic, we study the existence and uniqueness of solutions continuous at 0 for a boundary value problem of nonlinear q-difference equations with nonlocal and integral boundary conditions given by. The first result is based on Banach’s contraction principle and the second one on a fixed point theorem due to O’Regan. The existence of solutions for the problem (1.2) is shown by applying the nonlinear alternative for contractive maps
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