Stochastic stability of Cohen-Grossberg neural networks with unbounded distributed delays.
MSC 2010: 26A33, 34A08, 34K37
We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...
In this paper, we use a modification of Krasnoselskii’s fixed point theorem introduced by Burton (see [Burton, T. A.: Liapunov functionals, fixed points and stability by Krasnoseskii’s theorem. Nonlinear Stud., 9 (2002), 181–190.] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equation with variable delay The stability of the zero solution of this eqution provided that . The Caratheodory condition is used for the functions and .
By using successive approximation, we prove existence and uniqueness result for a class of neutral functional stochastic differential equations in Hilbert spaces with non-Lipschitzian coefficients
Effective sufficient conditions for oscillation and nonoscillation of solutions of some operator-differential equations with piecewise constant argument are found.