一类非齐次时滞微分方程概周期解的存在性

该文研究一类非齐次时滞微分方程的概周期解, 结合运用指数二分法, 给出了系统存在概周期解的一组充分条件.     

Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension

The fundamental equations of the problems of generalized thermoelasticity with one relaxation parameter including heat sources in infinite rotating magneto-thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace transform domain for a one dimensional problem. These equations have been solved by the eigenvalue approach to determine deformations, stress, and temperature. The results have been compared to those available in the existing literature. The graphs have been drawn to show the effect of rotation in the medium.     

On a Liouville phenomenon for entire weak supersolutions of elliptic partial differential equations

We study a new Liouville-type phenomenon for entire weak supersolutions of elliptic partial differential equations of the form A(u)=0 on , n2. Typical examples of the operator A(u) are the p-Laplacian for p>1, the mean curvature operator, and their well-known modifications.     

Mathematical modelling and computational analysis of enzymatic degradation of xenobiotic polymers

We study the enzymatic degradation of xenobiotic polymers mathematically. As a mathematical model, we derive a linear second-order hyperbolic partial differential equation which governs the evolution of the weight distribution with respect to the molecular weight. Given an initial weight distribution and a final weight distribution, we formulate a problem to determine a degradation rate. We establish a necessary and sufficient condition for which the problem has a local solution. We also introduce a numerical technique based on our analysis, and present a numerical result that we obtained applying weight distributions before and after enzymatic degradation of polyvinyl alcohol.     

The variational Lyapunov function and strict stability theory for differential systems

In this paper, we investigate strict stability of differential systems by variational Lyapunov function. We obtain some sufficient conditions and comparison theorems.     

The model theory of m‐ordered differential fields

In his Ph.D. thesis [7], L. van den Dries studied the model theory of fields (more precisely domains) with finitely many orderings and valuations where all open sets according to the topology defined by an order or a valuation is globally dense according with all other orderings and valuations. Van den Dries proved that the theory of these fields is companionable and that the theory of the companion is decidable (see also [8]). In this paper we study the case where the fields are expanded with finitely many orderings and an independent derivation. We show that the theory of these fields still admits a model companion in the language L = {+, –, ·, D, <₁, …, <_m, 1, 0}. We denote this model companion by CODF_m and give a geometric axiomatization of this theory which uses basic notions of algebraic geometry and some generalized open subsets which appear naturally in this context. This axiomatization allows to recover (just by putting m = 1) the one given in [4] for the theory CODF of closed ordered differential fields. Most of the technics we use here are already present in [2] and [4]. Finally, we prove that it is possible to describe the completions of CODF_m and to obtain quantifier elimination in a slightly enriched (infinite) language. This generalizes van den Dries' results in the “derivation free” case. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Remarks on Barbashin-Ezeilo Problem on third-order nonlinear differential equations

In this paper, we use the frequency domain criteria to initiate a general result on the Barbashin-Ezeilo Problem on third-order nonlinear differential equation. Earlier ideas of Burkin [I.M. Burkin, Orbital stability of second-kind limiting cycles for dynamical systems with cylindrical phase space, Differential Equations 29 (1993) 1262-1264], Leonov [G.A. Leonov, A frequency criterion for the existence of limit cycles of dynamical systems with cylindrical phase spaces, Differential Equations 23 (1987) 1375-1378] on the problem are being improved upon.     

A construction of real weight functions for certain orthogonal polynomials in two variables

H.L. Krall and I.M. Sheffer considered the problem of classifying certain second-order partial differential equations having an algebraically complete, weak orthogonal bivariate polynomial system of solutions. Two of the equations that they considered are

(x²+y)uxx+2xyuxy+y²uyy+gxux+g(y−1)uy=λu,     

Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the first order neutral functional differential equation of the form

(x(t)+Bx(t−δ)^)′=g₁(t,x(t))+g₂(t,x(t−τ))+p(t).     

Existence theorems for a class of nonlocal differential equations

A class of nonlocal second-order ordinary differential equations of the form

y^″(x)=f(x,y(x),(y○λ)(x),y^′(x))