Kasyanov P.O.

Trajectory Behavior of Weak Solutions of the Piezoelectric Problem with Discontinuous Interaction Function on the Phase Variable

The autonomous second order inclusion in a bounded domain, which is modeling the behavior of a class of the controlled piezoelectric fields with nonmonotonous potential, is studied. The investigated system describes not only controlled piezoelectric process with multivalued law “reaction-displacement”, but a wide class of controlled processes of Continuum Mechanics. Conditions on the parameters of the problem do not guarantee the uniqueness of solution of the corresponding Cauchy problem.

Nonmonotone penalty method for a class of multivariation inequalities with pseudomonotone type maps

We consider the class of multivariation inequalities in the infinitedimensional spaces with λ0 –pseudomonotone maps. Using the nonmonotone multivalued penalty method, we prove the existence of the solution for a wide range of problems. Furthermore, the apriory estimates for solutions are obtained.

Solutions properties for one class of parameterized operator inclusions

This paper provides the insights into the properties of solutions for parameterized operator inclusions with multi-valued maps of type. We prove the resolvability of such inclusions, weak compactness and parameter dependence of their solution. Moreover, we provide the example, illustrating the obtained results.

The periodic solutions for a class of differential-operator inclusions with Sk type maps

In this paper, we consider a class of evolution inclusions with Sk type maps. Using the Faedo–Galerkin method, the existence of periodic solutions was proved. To demonstrate the obtained generalizations, we provide a simple example.

On solvability for the second order nonlinear evolution equations with noncoercive [i]W[sub][lambda][sub]0[/sub][/sub][/i]-pseudomonotone maps

In this paper, we consider a class of the second order evolution equations with Wλ0-pseudomonotone maps. Using the Faedo-Galerkin method, the resolvability for a class of evolution equations with nonlinear noncoercive operators, in particular with variation calculus operators, is proved. Furthermore, the uniform priori estimations in Lq(S;V'σ) for derivatives are obtained.