A non-resonance problem for non-Newtonian fluids

In this article we study a highly nonlinear problem which describes a non-Newtonian fluid in a specific domain (symmetric channel). This fluid is subjected to pressure of known differences between two parallel plates. We establish the existence and uniqueness of a weak solution. Our solution method is based on a minimization technique when the nonlinearity is asymptotically on the left of the first eigenvalue of the operator k-Laplacian.