Maximum Principle for a Control Problem Governed by an Evolution Equation

We prove the maximum principle for an optimal control problem governed by the system

Oscillations of certain second order nonlinear differential equations

A second order nonlinear differential equation

The third mixed problem for the Sonin equation in a half space

We consider follwing mixed boundary-value problem:

On nonoscillation of canonical or noncanonical disconjugate functional equations

Qualitative comparison of the nonoscillatory behavior of the equations

On the asymptotic stability ofθ-methods for delay differential equations

Stability regions of -methods for the linear delay differential test equations

Uniformly convergent difference schemes for singularly perturbed parabolic diffusion-convection problems without turning points

We consider first the initial-boundary value problem for the parabolic equation

On the rapidly decreasing solutions for some systems of differential equations with unbounded coefficients

In this paper we continue the study of solvability of the non-homogeneous system of linear differential equations

The impact of unbounded swings of the forcing term on the asymptotic behavior of functional equations

Necessary and sufficient conditions have been found to force all solutions of the equation

Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation

The purpose of the paper is to study properties of solutions of the Cauchy problem for the equation under the assumption . General selfsimilar solutions are constructed. Moreover, for initial data with some decay at infinity, we determine the leading term of the asymptotics of solutions in which is described by either solutions of the linear heat equation or by particular selfsimilar solutions of the original equation.     

Asymptotic Formulas for the Solutions of Integro-Differential Equations

We study the problem of asymptotic integration of the linear integro-differential equation

On the oscillation and asymptotic behavior of the solutions of a certain system of differential-functional equations of neutral type

Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type

Jacobi elliptic functions and change of variable in a convolution

We solve the functional equation

On oscillation and asymptotic property of a class of third order differential equations

In this paper, oscillation and asymptotic behaviour of solutions of have been studied under suitable assumptions on the coefficient functions such that a(t 0, b(t) 0 and c(t) < 0.     

A problem of adaptive control with standard model

We consider the problem of adaptive control by a linear stochastic system with lag

A fourth order method for a singular two-point boundary value problem

Recently, Chawla et al. described a second order finite difference method for the class of singular two-point boundary value problems:

Critical Exponents for the Heat-Conduction Equation with Nonlocal,Nonlinear Perturbations

We study the conditions for the existence and nonexistence of global in time (t > 0), nonnegative solutions of the problem

On Lipschitz property of solutions of functional equations

In this work it is proved that under certain conditions the continuous vector-valued solutionsf of the functional equation

On the mixed problem for hyperbolic partial differential-functional equations of the first order

We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order where is a function defined by z _(x,y)(t, s) = z(x + t, y + s), (t, s) [–, 0] × [0, h]. Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.     

On quasi degree quadrature rules

Summary In this paper we examine quadrature rules for the integral which are exact for all with +d. We specify three distinct families of solutions which have properties not unlike the standard Gauss and Radau quadrature rules. For each integerd the abscissas of the quadrature rules lie within the closed integration interval and are expressed in terms of the zeros of a polynomialq _d(y). These polynomialsq _d(y), (d=0, 1, ...), which are not orthogonal, satisfy a three term recurrence relation of the type Q_d+1(y)=(y+_d+1)q_d(y)–_d+1yq_d–1(y) and have zeros with the standard interlacing property.This work was supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38