Abstract
This paper is devoted to the study of the existence of solutions for the strongly nonlinear parabolic equation
partial derivative u/partial derivative t + Au + g(x,t,u) = f(x,t),
where A is a Leray-Lions operator acted from V-infinity,V-p(.)(a(alpha), QT) into its dual. The nonlinear term g satisfies growth and sign conditions and the datum f is assumed to be in the dual space V-infinity,V-p(.)(a(alpha), QT).