二阶复域微分方程亚纯解的不动点与超级

研究了亚纯函数系数的二阶线性微分方程解的不动点及超级问题,得到了有关复域微分方程亚纯解的不动点性质,并且由于受到微分方程的制约,其性质与一般亚纯函数的不动点性质相比,显得十分有趣.     

关于二阶复微分方程解的幂和解的微分多项式的不动点

本文研究了以整函数为系数的二阶线性微分方程解的幂和解生成的微分多项式的不动点问题,得到:二阶线性微分方程解生成的微分多项式的不动点性质,由于受到微分方程的限制,与一般亚纯函数的不动点性质相比是十分有趣的.事实上,它们与解的增长性密切相关.     

中立抛物型时滞偏微分方程解振动的充要条件

本丈讨论一类多滞量中立抛物型时滞偏微分方程解的振动性质。获得了其一切解振动的充要条件；所得充要条件将时滞偏微分方程解的振动判别问题转化为时滞微分方程解的振动判别问题；指出了其与普通抛物型偏微分方程解的质的差异．     

二阶复域微分方程解的不动点与超级

文中首次研究了４种类型的整函数系数的二阶线性微分方程的解的不动点及超级问题,得到：复域微分方程解的不动点性质,由于受到微分方程的制约,与一般超越整函数的不动点性质相比,是十分有趣的．     

亚纯函数系数微分方程的解和小函数的关系

研究了一类亚纯函数为系数的二阶非齐次线性微分方程的解及其微分多项式和小函数的关系,并得到了这类微分方程解以及解的一阶,二阶导数与微分多项式的不动点性质.     

非线性抛物型时滞微分方程解振动的充要条件

讨论了一类多滞量非线性抛物型时滞微分方程解的振动性质，获得了其一切解振动的充要条件；指出了其与普通抛物型偏微分方程解的质的差异。     

再生核空间W_2~2(*)中积分-微分方程精确解的表示

该文定义了一个再生核空间W_2~2(*),在其中讨论了积分-微分方程解的存在唯一性,给出了积分-微分方程一个定解问题的精确解的表达式及由精确解得出近似解的性质.     

中立抛物型偏微分方程解的强迫振动

本文讨论一类多滞量中立抛物型偏微分方程解的振动性质 ,获得了其一切解振动的充分条件 ;指出了与普通抛物型偏微分方程质的差异 .     

二阶线性微分方程亚纯解的不动点与超级

本文研究了以亚纯函数为系数的二阶线性微分方程的解及其一阶和二阶导数的不动点及超级问题，得到：二阶线性微分方程亚纯解及其一阶和二阶导数的不动点性质，由于受到微分方程的限制，与一般亚纯函数的不动点性质相比是十分有趣的，事实上，它们与解的增长性密切相关。     

复线性微分方程解的增长性的几个结果

本文研究了复线性微分方程解的增长性问题.利用两类具有某种渐进增长性质的函数作为线性微分方程的系数,讨论了两类二阶线性微分方程解的增长性,获得了方程解为无穷级.这些结果推广了先前的一些结果.     

Oscillations of higher order differential equations of neutral type

In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of nth order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.     

Asymptotic Behaviour and Global Existence of Solutions for Some Classes of Nonlinear Parabolic Equations

The paper deals with the asymptotic behaviour and global existence of solutions for some classes of nonlinear parabolic equations in regard to the monotone properties of the nonlinear term. The asymptotic behaviour of the solutions of initial-boundary value problem for nonlinear parabolic equations is studied via the method of differential inequalities in order to obtain oscillation criterion for the solutions. Existence of extremal solutions of semilinear elliptic and parabolic equations is investigated via monotone iterative methods. The extremal solutions are obtained via monotone iterates.     

Large time behaviour of solutions to a class of non-autonomous, degenerate parabolic equations

We consider a class of non-autonomous, degenerate parabolic equations and we study the asymptotic behaviour of the solutions. Even if the equation depends explicitly upon the time, we prove that several asymptotic properties, valid for the autonomous case, are preserved in this more general situation. To our knowledge, it is the first time that the asymptotic behaviour of solutions to non-autonomous equations is studied.     

Symmetry analysis and optimal systems of generalized Chaplygin gas equations with a source term

The system of generalized Chaplygin gas equations with a coulomblike friction term has been investigated by using the famous Lie symmetry method. A direct and systematic algorithm based on the adjoint transformation and invariants of the admitted Lie algebras is then used to construct one- and two-dimensional optimal system of the Chaplygin gas equations. Inequivalent classes of group invariant solutions are then obtained using the one-dimensional optimal system. Further, the evolutionary behaviour of the weak discontinuity wave within the state characterized by one of the group invariant solutions is investigated in detail, and certain observations are noted in respect to their contrasting behaviour.     

Boundedness and stability of solutions to difference equations

This paper is concerned with the qualitative behaviour of solutions to difference equations. We focus on boundedness and stability of solutions and we present a unified theory that applies both to autonomous and nonautonomous equations and to nonlinear equations as well as linear equations. Our presentation brings together new, established, and hard-to-find results from the literature and provides a theory that is both memorable and easy to apply. We show how the theoretical results given here relate to some of those in the established literature and by means of simple examples we indicate how the use of Lipschitz constants in this way can provide useful insights into the qualitative behaviour of solutions to some nonlinear problems including those arising in numerical analysis.     

Periodic orbits of delay differential equations under discretization

This paper deals with the long-time behaviour of numerical solutions of delay differential equations that have asymptotically stable periodic orbits. It is shown that Runge-Kutta discretizations of such equations have attractive invariant curves which approximate the periodic orbit with the order of the method. The research by this author has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

A Finite-Dimensional Dynamical Model for Gelation in Coagulation Processes

Summary. We study a finite-dimensional system of ordinary differential equations derived from Smoluchowski's coagulation equations and whose solutions mimic the behaviour of the nondensity-conserving (geling) solutions in those equations. The analytic and numerical studies of the finite-dimensional system reveals an interesting dynamic behaviour in several respects: Firstly, it suggests that some special geling solutions to Smoluchowski's equations discovered by Leyvraz can have an important dynamic role in gelation studies, and, secondly, the dynamics is interesting in its own right with an attractor possessing an unexpected structure of equilibria and connecting orbits. Received April 26, 1997; revised October 3, 1997; accepted October 23, 1997     

Long-time behaviour of solutions of a class of nonlinear parabolic equations

In this paper, the long-time behaviour of solutions of a class of nonlinear parabolic equations is studied. It is shown that the solutions of initial-boundary value problem to the equations converge to a travelling wave solution of the equation or a self-similar solution of a Hamilton–Jacobi equation under certain conditions on initial and boundary values of the solutions.     

Long-time behaviour of solutions of a class of nonlinear parabolic equations

In this paper, the long-time behaviour of solutions of a class of nonlinear parabolic equations is studied. It is shown that the solutions of initial-boundary value problem to the equations converge to a travelling wave solution of the equation or a self-similar solution of a Hamilton–Jacobi equation under certain conditions on initial and boundary values of the solutions.     

Asymptotic Properties of the Electromagnetic Field in the External Schwarzschild Spacetime

. We study the asymptotic behaviour of the solutions to the vacuum Maxwell equations in the external Schwarzschild spacetime. The results are based on the extensive use of geometric considerations and the introduction of generalized energy estimates. We obtain the asymptotic behaviour along the null outgoing directions and we prove also some partial results concerning the behaviour along the timelike curves. Our techniques can be also used to control the asymptotic behaviour of the various derivatives of the Maxwell field and to obtain the asymptotic behaviour of the Weyl tensor fields, solutions of the "spin 2" equations.