In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the ...

We study oscillatory behavior of a class of second-order neutral di¤erential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional di¤erential inequalities. Our assumptions allow applications to di¤erential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results ...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

In this paper we present an analytic treatment of the inverse problem of reconstructing the internal electric conductivity of an in nite domain (the lower half space) from electrical measurements performed on its surface. To this end we transform the initial di erential equation into an integral equation, a procedure which has the advantage of permitting a simple discussion of the regularizatio...

In this paper we derive the sharp long time stability and error estimates of nite element approximations for parabolic integro di erential equations First the exponential decay of the solution as t is studied and then the semi discrete and fully discrete approximations are considered using the Ritz Volterra projection Other related problems are studied as well The main feature of our analysis i...

The stability of the ow of an incompressible, viscous uid through a pipe of circular cross-section, curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is ob...

We here provide two sided bounds for the density of the solution of a system of n di erential equations of dimension d, the rst one being forced by a non-degenerate random noise and the n− 1 other ones being degenerate. The system formed by the n equations satis es a suitable Hörmander condition: the second equation feels the noise plugged into the rst equation, the third equation feels the noi...

We present an extension of the lambda-calculus with di erential constructions. We state and prove some basic results (con uence, strong normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambda-calculus.

We present an overview of intrinsic integration schemes for diierential equations evolving on manifolds, paying particular attention to homogeneous spaces. Various examples of applications are introduced , showing the generality of the methods. Finally we discuss abstract Runge{Kutta methods. We argue that homogeneous spaces are the natural structures for the study and the analysis of these met...

We describe a MIMD parallel code to solve a general class of ordinary di erential equations, with particular emphasis on the large, sparse systems arising from space discretization of systems of parabolic partial di erential equations. The main goals of this work are sharp bounds on the accuracy of the computed solution and exibility of the software. We discuss the sources of error in solving d...