  In this paper, we consider the existence and uniqueness of weak solutions of
a nonlinear elliptic equation with a variable exponent, a monotonic type
operator and a convection term. With the topological degree theory, we prove
the existence of at least one weak solution under some Leray-Lions and growth
conditions. Moreover, we obtain the uniqueness of the solution of the problem
under some additional assumptions. Our results generalize and improve existing
results with another approach.
