In this work we examine the existence and uniqueness of the groundstate of a SU(N) x G(2) octonionic matrix model on a bounded domain of RN. The existence and uniqueness argument of the groundstate wavefunction follows from the Lax-Milgram theorem. Uniqueness is shown by means of an explicit argument which is drafted in some detail. (C) 2015 The Authors. Published by Elsevier B.V.