Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations

In this paper,the convergence of time-dependent Euler-Maxwell equations to compressible Euler-Poisson equations in a torus via the non-relativistic limit is studied. The local existence of smooth solutions to both systems is proved by using energy esti- mates for first order symmetrizable hyperbolic systems.For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order.The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order.     

Difference Equations∶ Detecting Oscillations via Higher Order Characteristic Equations

In these notes we introduce an alternative procedure to detect the presence of a wide range of oscillatory solutions-the exponential oscillatory ones-in both continuous-time and discrete linear difference equations. The technique is addressed to the scalar case of the linear two-delay difference equation, but it can be extended to other types of evolution equations including the nonlinear ones, in higher dimensions. In particular, we give an illustration of its applicability to the case of a simple two dimensional difference equation. Oscillatory solutions are presented in their closed formulae.     

Relations Between Linear Equations and Painlevé’s Equations

Painlevé equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas binding these approaches are derived. Symmetries demonstrated in the equations are also a subject of discussion.     

On Some Operator Equations

ＯｎＳｏｍｅＯｐｅｒａｔｏｒＥｑｕａｔｉｏｎｓＬｉＧａｎｇ（李刚）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ，２１０００８）ａｎｄＣｈｅｎｇＴａｏ（成涛）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...     

Linear Volterra Integral Equations

The Kurzweil-Henstock integral formalism is applied to establish the existence of solutions to the linear integral equations of Volterra-typewhere the functions are Banach-space valued. Special theorems on existence of solutions concerning the Lebesgu3 integral setting are obtained. These sharpen earlier results.     

Finding Roots of Equations

~~Finding Roots of Equations~~     

Iterative Solutions for a Non-monotone BinaryOperator Equations and Operator System of Equations

By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.     

What Are Equivalent Equations?

Theequationsx =6 38,4 32and 6 0 6 ,90 0 -x =- 31,532areequivalentequationsbecausetheyhavethesamesolu tions .Whenyouwritedownthestepstosolveanequation ,eachstepshouldbeanequationequivalenttotheequationsintheprevioussteps .ExampleMultiplechoice .Whichequationisnotequivalenttotheothers?(a)x +3=8　 (b) 2x =10　 (c) - 1=4 -x　 (d)x =5　 (e)x - 0 .4 =4 .96SolutionEquations (a) ,(b) ,(c)and (d)allhavethesinglesolution 5.Thesolutiontoequation (e)is5.36 .Equatin (e)isnotequivalenttotheothers .Ofalleq…     

Solutions of Indefinite Hammerstein Equations

Consider the following equation:For positive definite or quasi-positive definite kernel k(x,y),the theory of equa-tion(1)has much been developed.But up to now,little is known about the caseof indefinite kernels.In this paper we get several results of the latter type. Let G R~N have finite measure and f(x,u)satisfy Caratheodory condition,     

Invariant Tori of Duffing-type Equations

ＩｎｖａｒｉａｎｔＴｏｒｉｏｆＤｕｆｆｉｎｇ－ｔｙｐｅＥｑｕａｔｉｏｎｓＹｕａｎＸｉａｏｐｉｎｇ（袁小平）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ｐｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ），Ｂｅｉｊｉｎｇ，１００８７１ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣａｏＺｈｉｊｉａｎｇＲ...     

Some Results on Subelliptic Equations

In this paper, we consider the principal on R^n, and we find a comparison principle for such semi-linear sub-elliptic equation in the whole R^n and infinitely many positive solutions of the problem. eigenvalue problem for Hormander＇s Laplacian principal eigenvalues. We also study a related prove that, under a suitable condition, we have     

Splitting of Operators and Operator Equations

In this paper,we consider the splitting operators into the product of two positive operators.For given operators A and T ∈ B(H) with A≥0 and ■,if T can be splitted as T=AX for some positive operator X,then the existence of X and the properties of T are studied.The related research are the solutions of operator equations T=XAX and TX=XAX,which have some particular properties and broad applications in many fields.The conditions for the existence of solutions or idempotent solutions of these kinds ...     

Periodic Solutions for Nonlinear Diferential Equations

ＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｆｏｒＮｏｎｌｉｎｅａｒＤｉｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓＣｏｎｇＦｕｚｈｏｎｇ（从福仲）（ＯｆｆｉｃｅｏｆＭａｔｈｅｍａｔｉｃｓ，８６００３Ｕｎｉｔ，Ｃｈａｎｇｃｈｕｎ，１３００２２）ＭａｏＤｏｎｇｍｉｎｇ（...     

Oscillation of Neutral Equations withVariable Coefficients

51iIntroductionConsidertheneutralequationwithvariablecoefficientsInrecentyears,thedscillatotytheoryforneutralequathaiswelldeveloped.Inparticular,manydifferentsuffitientconditionsfortheoscillationofallsolutionsofEq.(l)areobtainedin[l-7j.Allthepapersmentionedexcept[6],however,alwaysassumeP(t)isinoneofthefOllowingranges:OSP(t)SlorP(t)2l.Ouraiminthispapertoeatablishnewsufficientcon-ditionsfortheoscillationofallsolutiOnsofEq.(l)underlessrestrictivehypothesesonP(t).Letm=max{Y,d}.Byasolutionof…     

On Contact Equivalence of Monge-Ampère Equations to Linear Equations with Constant Coefficients

We solve a problem of local contact equivalence of hyperbolic and elliptic Monge-Ampère equations to linear equations with constant coefficients. We find normal forms for such equations: the telegraph equation and the Helmholtz equation.     

Localization Problem for General Filtration Equations

ＬｏｃａｌｉｚａｔｉｏｎＰｒｏｂｌｅｍｆｏｒＧｅｎｅｒａｌＦｉｌｔｒａｔｉｏｎＥｑｕａｔｉｏｎｓＹｕａｎＨｏｎｇｊｕｎ（袁洪君）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）＆（Ｄｅ...     

Volterra-Type Equations in S + ′

Necessary and sufficient condition for the unique solvability of Volterra integro-differential equation in $S\prime _ + $ is given.     

Nonlinear Biharmonic Equations with Critical Potential

In this paper, we study two semilinear singular biharmonic equations： one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile, we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result.     

LaSalle''''s Theorem for Stochastic Differential Equations

In this paper, we establish a the LaSalle's theorem for stochastic differential equation based on Li's work, and give a more general Lyapunov function which it is more easy to apply. Our work has partly generalized Mao's work.     

Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.