Existence and nonexistence outcomes for a third-order q-difference equation

In this paper, using the Schauder and the Banach fixed point (FP) theorems, we examine the existence and uniqueness of solutions in the Banach space C([0, 1]) for a boundary value problem (BVP) of non-linear third-order q-difference equations with the q-integral boundary condition. Then, we impose the sufficient condition that allows us to deduce a nonexistence result. Furthermore, we offer some examples to support our main outcomes.