EXISTENCE AND UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF (2n+1)TH ORDER DIFFERENTIAL SYSTEM

In this paper we consider the problem ofllrmt cycles for thefollowing system【&一y＋6x＋a旷＋a。xy＋a。xy‘＋6xv‘”,(门)!i二 X( 一 by)．Ssstem(1)with k二 b二 0 was studiedin P叩er[1];Ifk 4 0 by transformation:y三 x;V二告;d,二 kdt,system(1)。二。can be trmslated Into the form studiedIn p。per IZ]三 System(1)With口1二 k二 0 W。S Studied ill paper k3]．Ifi System(1;SllPPOSe th。t:(1 ＞2 Is。11 lllteger,k / 0*d 6 / oi(2)。1。2 ＋。5 2 0,this assumption Is the same as that In paper[1];(3)w…     

On the Solutions of the Coupled Nonlinear Parabolic Equations

By means of the fixed point technique and integral estimation method, we study the solutions of periodic boundary value problem and initial value problem for the coupled nonlinear parabolic equations. The global classical solutions of the mentioned problems are shown to exists.     

Necessary and Sufficient Conditions of Existence and Uniqueness of Limit Cycles for a Polynomial System

In this paper, the following polynomial system is discussed:And the necessary and sufficient conditions of existence and uniqueness of limit cyclesare obtained.     

EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTIONS OF THE MODIFIED KS-CGL EQUATIONS FOR FLAMES GOVERNED BY A SEQUENTIAL REACTION

In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term |P|~2P is replaced with the generalized form |P|~(2σ)P,see [18]. The main novelty compared with [18] in this paper is to control the norms of the first order of the solutions and extend the global well-posedness to three dimensional space.     

一类广义Lienard方程的周期边值问题

利用整体反函数理论对一类广义Lienard方程x″ f(x,x′)x′ g(t,x,x′)=e(t)进行了研究,证明了周期解的存在唯一性,推广和改进了现有的结果.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE VISCOELASTIC EQUATIONS FOR KOITER SHELLS

In this paper,we consider the linearly viscoelastic equations for Koiter shells. Also,we prove the existence and uniqueness of the solution by Galerkin method.     

The Cauchy Problem for a Class of Coupled Systems Containing a Convolution Operator

Some results on the invariant regions ,existence and uniqueness of solutions to a class of integrodifferential systems are established. Applying these results to integrodifferential systems with a small parameter ε > 0, we obtain,in particular, some estimates of solutions uniform in ε > 0.     

浅谈二元函数的带Peano型余项的Taylor公式

本文讨论了二元函数带Peano型余项的泰勒公式及唯一性,例说其应用.     

Solution of the Navier–Stokes problem

A new a priori estimate for solutions to Navier–Stokes equations is derived. Uniqueness and existence of these solutions in for all is proved in a class of solutions locally differentiable in time with values in , where is the Sobolev space. By the solution a solution to an integral equation is understood. No smallness restrictions on the data are imposed.     

Signorini接触问题的边界变分不等式

本以Signorini接触问题为背景，讨论了变分不等式与边值问题的等价性，利用Green公式，基本解和基本解法向导数的性质，将区域型变分不等式化成等价的边界型变分不等式，并证明了边界变分不等式解的存在唯一性，为使用边界元方法数值求解提供理论依据。     

Cauchy's Problem for Degenerate Quasilinear Hyperbolic Equations with Measures as Initial Values

The aim of this paper is to discuss the Cauchy problem for degenerate quasilinear hyperbolic equations of the form \frac{∂u}{∂t} + \frac{∂u^m}{∂x} = -u^p, m > 1, p > 0 with measures as initial conditions. The existence and uniqueness of solutions are obtained. In particular, we prove the following results: (1) 0 < p < 1 is a necessary and sufficient condition for the above equations to have extinction property; (2) 0 < p < m is a necessary and sufficient condition for the above equations to have localization property of the propagation of perturbations.     

Existence and uniqueness of solutions of surface reconstruction problem

Surface reconstruction from scattered data is an important problem in such areas as reverse engineering and computer aided design.In solving partial differential equations derived from surface reconstruction problems,level-set method has been successfully used.We present in this paper a theoretical analysis on the existence and uniqueness of the solution of a partial differential equation derived from a model of surface reconstruction using the level-set approach.We give the uniqueness analysis of the cl...     

三维复Ginzburg-Landau方程的整体解的存在惟一性

在三维空间中研究带2σ次非线性项的复值Ginzburg—Landau方程(CGL) ut=ρu (1 iγ)△u-(1 iμ)|u|^2σu,通过先验估计的方法,在适当的σ的假设下,获得该方程周期边值问题整体解的存在性和惟一性．