We study the existence theory to quasistatic initial-boundary value problems with internal variables, which model the viscoelastic or viscoplastic behavior of solids at small strain. In these problems a system of linear partial differential equations coupled with a nonlinear system of differential equations or differential inclusions must be solved. The solution theory is based on monotonicity ...

Existence results for problems with monotone nonlinear boundary conditions obtained in the previous publications by the author for functional differential equations are transferred to the case of nonconvex differential inclusions with the help of the selection theorem due to A. Bressan and G. Colombo. The existence of solutions of boundary value problems for differential inclusions with possibl...

this paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. finally an example is given to illustrate the performance of the methods.

Forward viability and invariance of time-dependent differential inclusions are studied with the aid of generalized differentials. Contingent derivative is compared with a newer concept of generalized differential quotient. It is shown that the latter is more suitable for expressing criteria of viability and invariance, as it better describes the directions tangent to invariant trajectories of d...

In this work an existence theorem for nth-order ordinary differential inclusions is proved without the continuity of multi-valued functions. Our results are an improvement upon the existence results of Dhage et al. [B.C. Dhage, T.L. Holambe, S.K. Ntouyas, Upper and lower solutions for second order discontinuous differential inclusions, Math. Sci. Res. J. 7 (5) (2003) 206–212] and Agarwal et al....

The purpose of the course is to study several dynamics generated by strategic interactions in games. Among the topics are adaptive dynamics in evolutionary game theory, robust procedures for on-line algorithms and stochastic approximation. 1. Fictitious play Discrete time Continuous time and best reply dynamics 2. Replicator dynamics n populations One population Evolutionary Stable Strategies 3...

In this article we prove the substantiation of the method of averaging for the fuzzy integrodifferential inclusions with small parameter. Thereby we expand a circle of systems to which it is possible to apply Krylov-Bogolyubov method of averaging.