Turan, NihanAhin, Aynur2026-01-312026-01-3120252473-6988https://doi.org./10.3934/math.20251188https://hdl.handle.net/20.500.12662/10832In 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.eninfo:eu-repo/semantics/openAccessboundary value problemsq-difference equationsintegral-type boundary conditionsGreen's functionfixed point theoremsArticle10.3934/math.202511882-s2.0-1050228853662705711Q12704410WOS:001622414000002Q1