Quasi-linear functional differential equations with Property A

We study oscillatory properties of solutions of a functional differential equation of the form

(0.1)     

Asymptotically almost periodic solutions of abstract retarded functional differential equations of second order

We establish existence of asymptotically almost periodic mild solutions for a class of semi-linear second-order abstract retarded functional differential equations with infinite delay. Research supported in part by FONDECYT, grant 1050314.     

On very weak entire solutions of nonlinear partial differential equations

Let us consider the variational equation in R ⁿ

Existence theorems for nonlinear functional differential equations of neutral type

Conditions are found upon satisfaction of which the differential equation

STABILITY AND ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Itiswellknownthattheexistenceofalmostperiodicsolutionsiscloselyrelatedtothestabilityofsolutions.Forfunctionaldifferentialequationswithinfinitedelay,Y.Hin.[5'6]studiedtheproblemsontheexistenceofalmostperiodicsolutionsandthestability.However,therearefewpapersll2]dealingwithneutralfunctionaldifferentialequationswithinfinitedelay.Inthepresentpaper,forneutralfunctionaldifferentialequationswithinfinitedelay,weprovetheinherencetheoremfortheuniformlystableoperatorD(t),definethestabilitywithrespecttot…     

A methodology for supporting strategy implementation based on the VSM: A case study in a Latin-American multi-national

Soft OR tools have increasingly been used to support the strategic development of companies at operational and managerial levels. However, we still lack OR applications that can be useful in dealing with the “implementation gap”, understood as the scarcity of resources available to organizations seeking to align their existing processes and structures with a new strategy. In this paper we contribute to filling that gap, describing an action research case study where we supported strategy implementation in a Latin American multinational corporation through a soft OR methodology. We enhanced the ‘Methodology to support organizational self-transformation’, inspired by the Viable System Model, with substantive improvements in data collection and analyses. Those adjustments became necessary to facilitate second order learning and agreements on required structural changes among a large number of participants. This case study contributes to the soft OR and strategy literature with insights about the promise and constraints of this soft OR methodology to collectively structure complex decisions that support organizational redesign and strategy implementation.     

The averaging method and the asymptotic behavior of solutions to differential inclusions

We prove one version of the first Bogolyubov theorem for differential inclusions with multivalued mappings that satisfy certain one-sided constraints. We study the dependence of solutions to differential inclusions on the parameters.     

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

Stability and asymptotic stability of -methods for nonlinear stiff Volterra functional differential equations in Banach spaces

This paper is concerned with the stability and asymptotic stability of θ-methods for the initial value problems of nonlinear stiff Volterra functional differential equations in Banach spaces. A series of new stability and asymptotic stability results of θ-methods are obtained.     

Oscillation criteria and asymptotic properties of solutions of third‐order nonlinear neutral differential equations

The main goal of this article is to study the asymptotic properties and oscillation of the third‐order neutral differential equations with discrete and distributed delay. We give several theorems and related examples to illustrate the applicability of these theorems. Copyright © 2014 John Wiley & Sons, Ltd.     

Periodic solutions of abstract neutral functional differential equations with infinite delay

We establish the existence of mild solutions and periodic mild solutions for a class of abstract first-order non-autonomous neutral functional differential equations with infinite delay in a Banach space. This research was supported by FONDECYT-CONICYT, Grant 1050314.     

The characterization of a class of multivariate MRA and semi-orthogonal parseval frame wavelets

Let A be a d × d expansive matrix with ∣detA∣ = 2. This paper addresses Parseval frame wavelets (PFWs) in the setting of reducing subspaces of L²(R^d). We prove that all semi-orthogonal PFWs (semi-orthogonal MRA PFWs) are precisely the ones with their dimension functions being non-negative integer-valued (0 or 1). We also characterize all MRA PFWs. Some examples are provided.     

A geometric realization of quantum groups of type D

We geometrize quantum groups of type D in the spirit of Beilinson et al. (1990) [1].     

A semiexplicit method for numerical solution of functional differential algebraic equations

We study systems with delay effect that contain additional algebraic relations. We propose semiexplicit numerical methods of the Rosenbrock type. We prove the solvability of equations of a numerical model and estimate the order of the global error. The chosen parameters provide the third order of the error.     

On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations

In this paper, sufficient conditions have been obtained under which every solution of

Two solutions to a nonlinear Neumann problem without asymptotic conditions

We use critical point theory to establish the existence of at least two solutions to a nonlinear Neumann problem involving the one-dimensional p-Laplacian without assuming asymptotic conditions at infinity on the nonlinearity.     

Remarks on extremal solutions of differential equations with advanced argument

We show the existence of absolutely continuous extremal solutions to the problemx′(t)=f(t, x)h(t)))+g(t)),x(0)=x ₀, whereh is an arbitrary continuous deviated argument. Conditions for the uniqueness of solutions are given. Research partialy supported by grant UG BW 5100 - 5 - 0143 - 4     

Approximate solutions of abstract differential equations

The methods of arbitrarily high orders of accuracy for the solution of an abstract ordinary differential equation are studied. The right-hand side of the differential equation under investigation contains an unbounded operator which is an infinitesimal generator of a strongly continuous semigroup of operators. Necessary and sufficient conditions are found for a rational function to approximate the given semigroup with high accuracy. The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503.     

Periodic boundary value problem of functional differential equations with perturbation

By coincidence degree, the existence of solution to the periodic boundary value problem of functional differential equations with perturbation     

Oscillation and asymptotic behavior of third-order nonlinear neutral delay differential equations with distributed deviating arguments

This paper concerns the oscillation and asymptotic behavior of a class of third-order nonlinear neutral delay differential equations with distributed deviating arguments. By employing a generalized Riccati transformation and integral averaging technique, we establish some sufficient conditions to ensure that all solutions of the considered equations are either oscillatory or converge to zero, which extend and improve some known results in the literature.