On the Existence and Uniqueness of Solutions of a Fourth‐Order q ‐Difference Equation With Three‐Point Boundary Conditions

In this paper, we investigate the existence and uniqueness of solutions for a fourth‐order nonlinear q ‐difference equation with three‐point boundary conditions (BCs). First, the corresponding Green’s function is constructed, and its main properties are studied. Using this Green’s function, the boundary value problem (BVP) is transformed into an equivalent integral equation. The existence of at least one solution is established by applying Krasnosel’skii’s fixed point (FP) theorem, while the uniqueness result is obtained via the Banach FP theorem under suitable assumptions on the nonlinear term. Additionally, two examples are presented to illustrate the applicability of the main results. The obtained results contribute to the theory of higher order q ‐difference equations with BCs.