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Oscillation theorems for certain delay partial difference equations

2006
*
Applied Mathematics Letters
*

In this work we obtain some new

doi:10.1016/j.aml.2005.08.015
fatcat:smrwh34anzf2ne66tuvckgd6vq
*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] ). ...##
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Linearized oscillation theorems for certain nonlinear delay partial difference equations

1998
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Computers and Mathematics with Applications
*

This paper is concerned with the nonlinear

doi:10.1016/s0898-1221(97)00294-0
fatcat:iutovv5gsvfvhpugypeosccbnu
*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] . ...##
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Oscillation of systems of certain neutral delay parabolic differential equations

2003
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Journal of Applied Mathematics and Stochastic Analysis
*

Sufficient conditions are established

doi:10.1155/s1048953303000066
fatcat:arztke6f2nhnxilpazva4ramhi
*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. ...##
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Page 272 of Mathematical Reviews Vol. , Issue 99a
[page]

1991
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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. ...##
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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*. ...##
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Abstract Differential and Difference Equations

2010
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Advances in Difference Equations
*

Some new

doi:10.1155/2010/857306
fatcat:t7bt6bqa5jb6ffnqja7nevgise
*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*...##
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Page 3322 of Mathematical Reviews Vol. , Issue 2002E
[page]

2002
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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. ...##
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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*. ...##
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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. ...##
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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. ...##
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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. ...##
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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 ...

##
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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*. ...##
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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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