This paper proposes a method of discovering some kinds of di erential equations with interval coe cients, which characterize or explain numerical data obtained by scienti c observations and experiments. Such numerical data inevitably involve some ranges of errors, and hence they are represented by closed intervals in this paper. Based on these intervals, we design some interval inclusions which...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

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 ...

A non-oscillatory numerical scheme based on a general solution of unsteady advection–di usion equations is presented. A general solution for initial value problems of linear two-dimensional unsteady advection–di usion equations is obtained using the spectral method. The resulting numerical scheme is explicit with respect to time, and ful lls the Patankar’s positive coe cients condition for any ...

First order neutral di¤erential equations are studied and su‰cient conditions are derived for every solution to be oscillatory. Our approach is to reduce the oscillation of neutral di¤erential equations to the nonexistence of eventually positive solutions of non-neutral di¤erential inequalities. Our results extend and improve several known results in the literature.

Oberwolfach Tagungsbericht 26/1999 Partial Di erential Equations 13.06.1999 { 19.06.1999 This meeting was organized by L. C. Evans (Berkeley), S. M uller (MPI Leipzig) and E. Kuwert (Freiburg). The 22 delivered talks addressed a broad spectrum of questions for nonlinear partial di erential equations. Most of the considered problems arise in geometry or in physics, as for example submanifolds w...

This paper is concerned with linear uniformly elliptic and par abolic partial di erential equations in divergence form It is assumed that the coe cients of the equations are random variables constant in time The Green s functions for the equations are then random variables Regularity properties for expectation values of Green s functions are obtained In par ticular it is shown that the expectat...

We study a new class of backward stochastic di€erential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial di€erential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.

In this work we consider the problem of control of mechanical systems subject to unilateral constraints. Impulsive forces arise whenever the constraints become active and these forces give rise to nonsmooth dynamics. The dynamics of the system is de ned by a set of di erential equations with discontinuous righthand side using Hamilton's equations of motion. A nonlinear transformation is applied...

In this paper we discuss the formulation of the governing equations that describe ow of uids in porous media Various types of uid ow ranging from single phase ow to compositional ow are considered It is shown that all the di erential equations governing these types of ow can be e ectively rewritten in a fractional ow formulation i e in terms of a global pressure and saturation or saturations an...