The Navier problem involving the p-biharmonic and the Leray-Lions operators
with weights is considered in this paper. Using the theory of weighted
Sobolev spaces and the Browder-Minty theorem to show the existence and
uniqueness of weak solution to this problem. Firstly, we transform our
problem into an equivalent operator equation; secondly, we use the
Browder-Minty theorem to prove the existence and uniqueness of a weak
solution to the problem concerned.