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A system of two operator equations is considered - one of pseudomonotone typeand the other of strongly monotone type - both being strongly coupled.Conditions are given that allow to reduce the solvability of this system to asingle operator equation for a pseudomonotone mapping. This result is appliedto a coupled system consisting of a parabolic equation of forth order in spaceof Cahn-Hilliard type and a nonlinear elliptic equation of second order to aquasi-steady mechanical equilibrium. Using an appropriate notation of weaksolutions and a framework for evolution equations developed by Gr\"oger, thesystem is reduced to a single parabolic operator equation and the existence ofsolutions are shown under restrictions on the strength of the coupling.

Existence for coupled pseudomonotone-strongly monotone systems and application to a Cahn-Hilliard model with elasticity