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OSCILLATION CRITERIA FOR NONLINEAR SECOND ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

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Chinese Annals of mathematics,Series B 1996年第1期17卷 89-102页

作者： zhang binggen ZHAO TAO B. S. LALLI (department of {3., ocean university of qingdao, qingdao 266003. China.)(department of {3., Arizona State university, U.S.A.)(Departmemt of {3., university of Saskatchewan, Canada.) 青岛海洋大学数学系山东青岛 Arizona State university 美国 university of Saskatchewan 加拿大

The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are establi... 详细信息

关键词： Oscillation Nonlinear elliptic equation Riccati inequality

An improvement in stability of delay difference systems

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Chinese Science Bulletin 1998年第7期43卷 544-547页

作者： zhang Shunian department of applied {3., Shanghai Jiaotong university, Shanghai 200240, China department of applied mathematics Shanghai Jiaotong University Shanghai China

A new result on the stability of delay difference equations is established, in which a kind of weighted norm for x is adopted in order to estimate the upper bound of Liapunov functional.

关键词： delay difference systems uniform asymptotic stability in terms of two measures Liapunov functionals.

Almost periodic solutions of difference systems

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Chinese Science Bulletin 1998年第24期43卷 2041-2046页

作者： zhang Shunian department of applied {3., Shanghai Jiaotong university, Shanghai 200240, China department of applied mathematics Shanghai Jiaotong University Shanghai China

For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient matrix and the nonhomogeneous term. The obtained result confirms not only the existence, but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution. As an application, a criterion on the existence of almost periodic solutions of the second order difference equations is derived.

关键词： difference systems mean values of almost periodic sequences almost periodic solutions existence uniqueness uniform asymptotic stability

Centralizers and Iterate Radicals of Morse-Smale Diffeomorphisms of the Circle

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Acta Mathematica Sinica,English Series 1995年第1期11卷 1-11页

作者： zhang Meirong department of applied {3. Tsinghua university Beijing,100084 China department of applied mathematics Tsinghua University Beijing People's Republic of China

In this paper,we will use the embedding flows in[1],[2]to give a complete descrip- tion of the smooth centralizers and iterate radicals of all C^r(r≥2)Morse-Smale diffeomorphisms of the circle S^*** a result,we prove... 详细信息

关键词： Centralizers and Iterate Radicals of Morse-Smale Diffeomorphisms of the Circle TDFs

New Complexiton Solutions of (2+1)-Dimensional Nizhnik-Novikov-Veselov Equations

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Communications in Theoretical Physics 2006年第9期46卷 407-414页

作者： zhang Yuan-Yuan,~+ ZHENG Ying, zhang Hong-Qing department of {3. mathematics, Dalian university of Technology, Dalian 116024, China department of applied mathematics Dalian University of Technology Dalian 116024 China

In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.

关键词： rational expansion method (2+1)-dimensional Nizhnik Novikov-Veselov equations complexiton solutions

Formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic sextic fields

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Chinese Science Bulletin 1998年第10期43卷 824-826页

作者： LIU Tong department of applied mathematics, Tsinghua {3., Beijing 100084, China department of applied mathematics Tsinghua University Beijing China

Let K 6 be a real cyclic sextic number fields, and K 2, K 3.be its quadratic and cubic subfields. Let h(L) denote the ideal class number of field L. Seven congruences for h -=h(K 6)/h(K 2)h(K 3. are obtained. In particular, when conductor f\-6 of K 6 is prime p, then Ch -≡B p-16B 5(p-1)6 (mod p), where C is an explicitly given constant, and B n is the Bernoulli number. These results for real cyclic sextic fields are an extension of results for quadratic and cyclic quartic fields obtained by Ankeny_Artin_Chowla, Kiselev, Carlitz, Lu Hongwen, zhang Xianke from 1948 to 1988.

关键词： real cyclic sextic number fields class number fundamental relative unit.

Quantitative result on stability for delay difference systems

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Chinese Science Bulletin 1997年第22期42卷 1858-1861页

作者： zhang Shuniandepartment of applied {3., Shanghai Jiaotong university, Shanghai 200240, China department of applied mathematics Shanghai Jiaotong University Shanghai China

IN ref. [1] we have established the stability criteria for the finite delay difference systems ofthe general form in terms of the discrete Liapunov functionals as well as Liapunov *** then, some other results have app... 详细信息

关键词： quadratic delay difference systems uniform stability uniform asymptotic stability stability region asymptotic stability region.

ON UNIFORM ASYMPTOTIC STABILITY OF INFINITE DELAY DIFFERENCE EQUATIONS

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Chinese Annals of mathematics,Series B 2001年第4期22卷 495-502页

作者： zhang SHUNIAN department of applied {3., Shanghai Jiaotong university Shanghai 20003., China. E-mail: snzhang@*** department of applied mathematics Shanghai Jiaotong University Shanghai 200030 China

For the infinite delay difference equations of the general form, two new uniform asymptotic stability criteria are established in terms of the discrete Liapunov functionals.

关键词： Infinite delay difference equations Uniform asymptotic stability g-uniform asymptotic stability Discrete Liapunov functionals

The Evaluation of Connection Coefficients on an Interval

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 252-255页

作者： Xiaolin ZHOU and Wu zhang(department of applied {3., Xi’an Jiao Tong university, Xi’an 710049, China) department of applied mathematics Xi'an Jiaotong University Xi'an 710049 China

A connection coefficient is an interval of products of wavelet basis functions,their derivatives and their translates. It can be used to solve PDEs numerically by the wavelet- Galerkin method. This paper presents an e... 详细信息

关键词： connection coefficients wavelets