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For a wide class of systems of variational equations depending on parameters with nonmonotone operators in a space real reflexive Banach space, we study the solvability, the existence of solutions with every components different to zero, the existence of multiple solutions and, in the omogeneous case, the existence of solutions with every positive components when Wl is a vector lattice according to the fibering method. We obtain results which have many different applications. For example, they can be used in order to study Dirichlet and Neumann problems and to check ODE periodic solutions

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We consider autonomous evolution inclusions and hemivariational inequalities with nonsmooth dependence between determinative parameters of a problem. The dynamics of all weak solutions defined on the positive semiaxis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. New properties of complete trajectories are justified. We study classes of mathematical models for geophysical processes and fields containing the multidimensional “reaction-displacement” law as one of possible application. The pointwise behavior of such problem solutions on attractor is described.

No abstract