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Oscillation theorems for certain delay partial difference equations

B.G. Zhang, Y.H. Wang
2006 Applied Mathematics Letters  
In this work we obtain some new oscillation criteria for certain delay partial difference equations with continuous arguments by some new techniques.  ...  In particular, the oscillation of partial difference equations with continuous arguments has been investigated in some papers [2] [3] [4] [5] .  ...  Introduction The qualitative analysis of partial difference equations has received much attention in the past few years (see the survey paper [1] ).  ... 
doi:10.1016/j.aml.2005.08.015 fatcat:smrwh34anzf2ne66tuvckgd6vq

Linearized oscillation theorems for certain nonlinear delay partial difference equations

B.G. Zhang, J.S. Yu
1998 Computers and Mathematics with Applications  
This paper is concerned with the nonlinear delay partial difference equation &+l,n + &"+I -&w +pm,nf (Am-k,n-1) = 0, where k and 1 are nonnegative integers and m, n = 0, 1, . . . .  ...  Some linearized oscillation theorems for this equation are obtained, i.e., we will prove that under some conditions on f, this equation haa the same oecillatory character as an eaeociated linear equation  ...  / -Q2)) = 0. ( 1.2) The oscillation of the delay partial differential equation ( 1.2) has been investigated by Tramov [4] .  ... 
doi:10.1016/s0898-1221(97)00294-0 fatcat:iutovv5gsvfvhpugypeosccbnu

Oscillation of systems of certain neutral delay parabolic differential equations

Wei Nian Li, Bao Tong Cui, Lokenath Debnath
2003 Journal of Applied Mathematics and Stochastic Analysis  
Sufficient conditions are established for the oscillation of systems of neutral delay parabolic differential equations. These results are illustrated by some examples.  ...  the partial differential equations of different types.  ...  They have obtained sufficient conditions for the oscillation of the system of delay hyperbolic partial differential equations with examples.  ... 
doi:10.1155/s1048953303000066 fatcat:arztke6f2nhnxilpazva4ramhi

Page 272 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
[Yu, Jian She] (PRC-HUN-AM; Changsha) Linearized oscillation theorems for certain nonlinear delay partial difference equations. (English summary) Comput. Math. Appl. 35 (1998), no. 4, 111-116.  ...  Summary: “Some new oscillation criteria for the second-order nonlinear delay difference equations A*y, + Py f (yn) =0 are established.  ... 

Page 8873 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
[Agarwal, Ravi P.] (1-FIT; Melbourne, FL) The oscillation and stability of delay partial difference equations. (English summary) Advances in difference equations, IV. Comput. Math.  ...  ng — 1} for some no € N = {0,1,2,...} and for every me N.” 2004k:39010 39A05 Tian, Chuanjun; Zhang, Jihong |Zhang, Ji Hong] Exponential asymptotic stability of delay partial difference equations.  ... 

Abstract Differential and Difference Equations

G. M. N'Guérékata, T. Diagana, A. Pankov
2010 Advances in Difference Equations  
Some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations and nonlinear delay dynamic equations on a time scale T, are established, improving some known results for  ...  oscillation of second-order nonlinear delay dynamic equations on time scales.  ...  Some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations and nonlinear delay dynamic equations on a time scale T, are established, improving some known results for  ... 
doi:10.1155/2010/857306 fatcat:t7bt6bqa5jb6ffnqja7nevgise

Page 3322 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
In this review article the author presents several known necessary and sufficient conditions for the oscillation of all solutions of certain delay partial difference equations.  ...  Various types of comparison theorems are also derived.” 2002¢:39035 39A10 Yang, Yu Hua Forced oscillation for delay difference equations. (Chinese. English and Chinese summaries) J. Hebei Norm. Univ.  ... 

Page 5762 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
This paper will be very useful for those researchers interested in oscillation theorems for partial difference equations. Allan C.  ...  The partial difference equations considered are discrete analogues of certain functional partial differential equations.  ... 

Page 1743 of Mathematical Reviews Vol. , Issue 81E [page]

1981 Mathematical Reviews  
Finally, the authors give oscillation theorems for bounded solutions of even order differential equations with deviating arguments. Ch. G. Philos (Ioannina) Burton, T. A.  ...  Stability theory for delay equations. Funkcial. Ekvac. 22 (1979), no. 1, 67-76.  ... 

Page 203 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
Summary: “Some comparison theorems and oscillation criteria are established for the neutral difference equation A(x, +CXn—m) + PnXn—k = 0, n=0,1,2,---, as well as for certain neutral difference equations  ...  [Zhang, Bing Gen] Oscillation and comparison theorems for certain neutral difference equations. (English summary) J. Austral. Math. Soc. Ser. B 34 (1992), no. 2, 245-256.  ... 

Page 4732 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
[Zhang, Bing Gen] (PRC-QUO-AM; Qingdao) Oscillation theorems for certain nonlinear delay partial difference equations. Nonlinear Anal. 41 (2000), no. 3-4, Ser. A: Theory Methods, 447-454.  ...  A sufficient condition for the oscillation of (1) is given, which can be regarded as a generalization of the relevant known result for delay difference equations without impulse.  ... 

List of contents

2002 Computers and Mathematics with Applications  
for Second-Order Quasilinear Functional Differential Equations Oscillation Theorems of Second-Order Nonlinear Neutral Delay Difference Equations with Impulses Numerical Verification of Boundary  ...  Solitonic Features of a Nonintegrable (3 + l)- Dimensional Jimbo-Miwa Equation Oscillation Theorems for Nonlinear Second-Order Differential Equations 539 545 Coefficients for Studying One-Step  ...  Numerical Study for Two-Point Boundary Value Problems Using Green's Functions  ... 
doi:10.1016/s0898-1221(02)80027-x fatcat:xvuiqiphbrc5hmnfs5xeh4canq

Page 7876 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
As an application, we establish the existence of radial solutions of certain partial difference equation.  ...  The paper gives sufficient conditions for all solutions of a scalar linear delay difference inequality of the type Xn41 — Xn + PnXn—k < 0 to oscillate.  ... 

Page 327 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
) ; Deng, Xing Hua (PRC-QUO-AM; Qingdao) The stability of certain partial difference equations.  ...  Sufficient conditions for this equation to be stable are derived. The stability of certain nonlinear partial difference equations is also studied.”  ... 

Page 3815 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
and differential-difference equations 94¢:34121 949:34118 34K15 34K40 Hou, Zhan Yuan (PRC-HBN; Shijiazhuang) Oscillation and small solutions of autonomous linear neutral equations.  ...  (Russian) Partial differential equations (Russian), 135-139, ““Obrazovanie’’, St. Petersburg, 1992.  ... 
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