Multivalued Dynamics of Solutions of Autonomous Operator Differential Equations with Pseudomonotone Nonlinearity

We consider nonlinear autonomous operator differential equations with pseudomonotone dependence between the defining parameters of the problem and study the dynamics of all weak solutions on the positive time semiaxis. We prove the existence of a trajectory and a global attractor and study their structure. As a possible application, we consider the class of high-order nonlinear parabolic equations.