Second-order neutral stochastic evolution equations with heredity.
Second-order sufficient conditions for strong solutions to optimal control problems
In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure a fortiori that the reference trajectory...
Semi-discrete transform
Semigroup approach to semilinear partial functional differential equations with infinite delay.
Semilinear fractional order integro-differential equations with infinite delay in Banach spaces
This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski’s measure of noncompactness and Mönch’s fixed point theorem. An example to illustrate the applications of main results is given.
Semilinear functional differential equations of fractional order with state-dependent delay.
Semilinear Neutral Functional Integrodifferential Inclusions
Set differential equations with causal operators.
Sharp inequalities for periodic functions.
Simultaneous solutions of a system of Abel equations and differential equations with several deviations
Singular positone and semipositone boundary value problems of second order delay differential equations
In this paper we present some new existence results for singular positone and semipositone boundary value problems of second order delay differential equations. Throughout our nonlinearity may be singular in its dependent variable.
Singularly perturbed set of periodic functional-differential equations arising in optimal control theory
We consider the singularly perturbed set of periodic functional-differential matrix Riccati equations, associated with a periodic linear-quadratic optimal control problem for a singularly perturbed delay system. The delay is small of order of a small positive multiplier for a part of the derivatives in the system. A zero-order asymptotic solution to this set of Riccati equations is constructed and justified.
Smooth dependence on parameters for some functional-differential equations.
Smooth Gevrey normal forms of vector fields near a fixed point
We study germs of smooth vector fields in a neighborhood of a fixed point having an hyperbolic linear part at this point. It is well known that the “small divisors” are invisible either for the smooth linearization or normal form problem. We prove that this is completely different in the smooth Gevrey category. We prove that a germ of smooth -Gevrey vector field with an hyperbolic linear part admits a smooth -Gevrey transformation to a smooth -Gevrey normal form. The Gevrey order depends on...
Smoothness of the attractor of almost all solutions of a delay differential equation [Book]
Solution of multi-delay systems via combined block-pulse functions and Legendre polynomials.
Solution semigroup and invariant manifolds for functional equations with infinite delay
It is proved that parabolic equations with infinite delay generate -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.
Solutions and Green's functions for boundary value problems of second-order four-point functional difference equations.
Solutions of an advance-delay differential equation and their asymptotic behaviour
The paper considers a scalar differential equation of an advance-delay type where constants , , and are positive, and and are arbitrary. The behavior of its solutions for is analyzed provided that the transcendental equation has a positive real root. An exponential-type function approximating the solution is searched for to be used in proving the existence of a semi-global solution. Moreover, the lower and upper estimates are given for such a solution.
Solutions of the neutral differential-difference equation .