The Algebraic Criteria for the All-delay Stabilityof Two-dim ensional Degenerate Differential System swith Delay

This paper give the algebraic criteria for all delay stability of two dimensional degenerate differential systems with delays and give two examples to illustrate the use of them.

FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.

THE SUFFICIENT AND NECESSARY CONDITIONS OF UNCONDITIONAL STABILITY AND THE DELAY BOUND OF THE THIRD-ORDER NEUTRAL DELAY DIFFERENTIAL EQUATION

In this paper, the sufficient and necessary conditions of the unconditional stability, and the delay bound of the third-order neutral delay differential equation with real constant coefficients are given. The conditions are brief and practical algebraic criterions Furthermore, we get the delay bound.

LYAPUNOV-LIKE EXPONENTIAL STABILITY AND UNSTABILITY OF DIFFERENTIAL-ALGEBRAIC EQUATION

In this paper, Lyapunov-like exponential stability and unstability of differentialalgebraic equation are considered from the viewpoint of stability of system motion, and the criteria of exponential stability and unstability of nonlinear nonautonomous differential-algebraic equation are given by using Lyapunov-like function similar to ordinary differential equation.

On the growth of transcendental entire solutions of algebraic differential equations

In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where a(z), b_i(z) (0<- i <=2) and d_j (z) (0<=j<= 3) are allpolynomials, and this equation relates closely to the following well-known algebraic differentialequation C(z,w)w'~2 + B(z,w)w' + A(z,w) =0, where G(z,w)not ident to 0, B(z,w) and A(z,w) are threepolynomials in z and w. We give relationships between the growth of entire solutions and the degreesof the above three polynomials in detail.

THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS

We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.

ON THE GROWTH OF SOLUTIONS OF HIGHER-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS

Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.

Generalized Higher-Order Algebraic Differential Equations with Admissible Algebroid Solutions

Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.

ON ALGEBRAIC SOLUTIONS OF THE SECOND-ORDER COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE ALGEBRAIC ELEMENT COEFFICIENTS

The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.

ALGEBRAIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

Using value distribution theory and techniques,the problem of the algebroid solutions of second order algebraic differential equation is investigated.Examples show that the results are sharp.

On the Order of the Solutions of Systems of Complex Algebraic Differential Equations

This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.

SOlvaBILITY OF HIGHER INDEX TIME-VARYING LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some equivalent system,,; are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems for higher index DAEs are proposed.

Efficient Numerical Methods for Solving Differential Algebraic Equations

This research aims to solve Differential Algebraic Equation (DAE) problems in their original form, wherein both the differential and algebraic equations remain. The Newton or Newton-Broyden technique along with some integrators such as the Runge-Kutta method is coupled together to solve the problems. Experiments show that the method developed in this paper is efficient, as it demonstrates that implementation of the method is not difficult, and such method is able to provide approximate solutions with ease within some desired accuracy standards.

ON HYPER-ORDER OF MEROMORPHIC SOLUTIONS OF FIRST-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS

The authors give a precise estimate of the hyper-order of meromorphic solutions of general first-order algebraic differential equations.

GROWTH OF MEROMORPHIC SOLUTIONS OF SOME ALGEBRAIC DIFFERENTIAL EQUATIONS

In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases.

A NEW ALGORITHM FOR SOLVING DIFFERENTIAL/ALGEBRAIC EQUATIONS OF MULTIBODY SYSTEM DYNAMICS

The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding discretization method is presented, and the results can be used to implementation of various numerical integration methods. A numerical example is presented finally.

A NOTE ON MALMQUIST-YOSIDA TYPE THEOREM OF HIGHER ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS

In this article, we give a simple proof of Malmquist-Yosida type theorem of higher order algebraic differential equations, which is different from the methods as that of Gackstatter and Laine [2], and Steinmetz [12].

ALGEBRAIC DIFFERENTIAL INDEPENDENCE CONCERNING THE EULER Γ-FUNCTION AND DIRICHLET SERIES

This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.

On the Counting Functions of Meromorphic Solutions of Systems of Higher-order Algebraic Differential Equations

Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.

ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM

In this article, linear regular index 2 DAEs A（t）[D（t）x（t）]＇ ＋ B（t）x（t） = q（t） are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1 DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given.