January 2023
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Publications (114)
September 1997
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33 Reads
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3 Citations
this paper is to develop an existence theory enabling us to construct various types of oscillatory and nonoscillatory solutions of neutral equations of the form (A). We make use of the observation that the associated unperturbed equation
December 1996
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4 Reads
August 1996
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31 Reads
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12 Citations
Computers & Mathematics with Applications
Some new oscillation results for difference equations of the form (1.1), and forced difference equations of the form (1.2), are established. The results obtained are discrete analogues of some known results for delay differential equations.
May 1996
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5 Reads
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3 Citations
Asymptotic and oscillatory properties of solutions of mth order nonlinear difference equations of the form D m y n +p n f(n,y n )=g(n,y n ) are investigated. The obtained results generalize some of the results of B. Szmanda [J. Math. Anal. Appl. 109, 22-30 (1985; Zbl 0589.39003)] for second order difference equations.
January 1996
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14 Reads
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22 Citations
Journal of Mathematical Analysis and Applications
Some oscillation criteria are established for forced neutral difference equations of the form Δ(xn + pxn+δk − qnƒ(xτn) = Fn and Δ2(xn + pxn+δk − qnƒ(xτn) = Fn. The results remain valid even when Fn = 0.
January 1996
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8 Reads
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19 Citations
Chinese Annals of Mathematics Series B
The second order elliptic differential equations Li(y; x) = ∑i,j=1n Di[Aij(x)Djy]+p(x)f(y) = 0 (1.1) and L2(y; x) = δy+p(x)|y|γsigny = 0, 1 ≠ γ > 0 (1.2) 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 established.
October 1995
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3 Reads
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24 Citations
Acta Mathematicae Applicatae Sinica
Sufficient conditions are established for the oscillation of some hyperbolic equations with deviating arguments under various boundary conditions.
June 1995
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14 Reads
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12 Citations
Applied Mathematics and Computation
The asymptotic and oscillatory behavior of solutions of second order difference equations with deviating argument of the form is studied. Examples are inserted to illustrate the results.
March 1995
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6 Reads
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20 Citations
Quarterly of Applied Mathematics
Necessary and sufficient conditions are presented for the oscillation of all positive solutions of the multiplicative delay logistic equation about the positive equilibrium K K . The cases when r ( t ) = r r\left ( t \right ) = r and g j ( t ) = t − τ j {g_j}\left ( t \right ) = t - {\tau _j} or g j ( t ) = [ t − k j ] {g_j}\left ( t \right ) = \left [ {t - {k_j}} \right ] , [•] denoting the greatest integer function, where r , τ j r, {\tau _j} , and k j {k_j} are positive constants, j = 1 , 2 , . . . , m j = 1, 2,...,m , are also included.
Citations (72)
... For linear NDEs, Gopalsamy et al. [39] established adequate conditions for every solution to oscillate, which are derived along with some comparison results. Candan [40] studied the oscillatory properties of mixed NDEs with distributed deviating arguments. ...
- Citing Article
January 1992
Czechoslovak Mathematical Journal
... Recently there has been a great interest in studying the oscillatory and asymptotic behavior of third order differential equations, see for example [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23], and the references cited therein. In [1,4,7,8,9,15,20,23], the authors studied the oscillatory behavior of solutions of equation (1.1) when b(t) ≡ 0, c(t) ≡ 0 and p(t) ≡ 0. In [5,6,10,11,17,18,19,21], the authors studied the oscillatory behavior of solutions of equation (1.1) when c(t) ≡ 0 and p(t) ≡ 0. In [2,13,14,22], the authors discussed the oscillatory behavior of all solutions of equation (1.1) when α = β = γ = 1. ...
- Citing Article
January 1988
Czechoslovak Mathematical Journal
... During the past period, many papers appeared on the oscillatory behavior of differential equations of neutral and delay type. Investigations by Zhang et al. [11], Li et al. [12][13][14][15], Baculikova et al. [16], and Grace and Lalli [17] have yielded techniques and methodologies aimed at enhancing the oscillatory attributes of these equations. Furthermore, the work of Zhang et al. and Agarwal et al. [6,[18][19][20][21] has expanded this inquiry to encompass differential equations of the neutral variety. ...
- Citing Article
January 1984
Proceedings of the American Mathematical Society
... The oscillatory theory as a part of the qualitative theory of differential equations has been developed rapidly in the last decades, and there has been a great deal of work on the oscillatory behavior of differential equations; see e.g. (Agarwal et al. 2010;Beqiri and Koci 2012;Bihari 1963;Elabbasy and Elsharabasy 1997;Elabbasy and Elhaddad 2007;Grace et al. 1984Grace et al. , 1988Grace and Lalli 1987, 1989, 1990Grace 1989Grace , 1990Grace , 1992Greaf and Spikes 1986;Graef et al. 1978;Lee and Yeh 2007;Kamenev 1978;Kartsatos 1968;Li and Agarwal 2000;Meng 1996;Nagabuchi and Yamamoto 1988;Ohriska and Zulova 2004;Ouyang et al. 2009;Philos 1983Philos , 1984Philos , 1985Remili 2010;Tiryaki and Basci 2008;Tiryaki 2009;Temtek and Tiryaki 2013;Yan 1986;Yibing et al. 2013a, b;Zhang and Wang 2010). Remili (2010), studied the equation Zhang and Wang (2010), studied the following equation ...
- Citing Article
January 1987
... Using (3) and (5) in (16) we get ...
- Citing Article
January 1987
Bollettino della Unione Matematica Italiana B
... where υ ≥ υ 0 . Our main aim is to complement and improve the results in [19][20][21]. To motivate that, we briefly review and put into context those and related results. ...
- Citing Article
January 1986
... In this spirit our main result unifies some earlier Kartsatos' results on the maintenance of oscillations under the effect of a "small" or "periodic-like" forcings and at the same time extends them to more general forcing functions. For other related results concerning Eq. (1) and corresponding functional differential equations and inequalities we refer the reader to the papers of Chen and Yeh [2,3], Foster [4], Grace and Lalli [5,6], Jaros [7,8], Kawano, Kusano and Naito [13], Kusano et al. [14][15][16], McCann [17], Onose [18,19] and True [21]. ...
- Citing Article
January 1984
Houston Journal of Mathematics
... The results we obtain are discrete analogues of the results given in [14,15]. For general background on difference equations, one can refer to [16,17] ...
- Citing Article
January 1989
Indian Journal of Mathematics
... The presence of the damping term in (1.8) calls for a modified approach to the study of the oscillatory properties of solutions. A number of oscillation criteria for (1.8) can be found, for example, in papers by Grace [10,12], Grace and Lalli [13][14][15][16][17][18][19][20][21], Grace, Lalli and Yeh [22], Kirane and Rogovechenkov [30,31], Li and Agarwal [39], Li and Zhang [41], Rogovechenkov [45], Wong [52], Yan [54] and Yeh [55]. However the common restriction f 0 (x) ≥ k > 0 is required, which does not hold, for example, for ...
- Citing Article
January 1987
Bulletin of the Polish Academy of Sciences Mathematics
... He was able to provide conditions that guarantee the oscillation of all bounded solutions. By establishing a criterion that guarantees the oscillation of all solutions, Grace and Lalli [19] tested the oscillation of DDEs using the Riccati technique. Later, Zhang and Ladde [20] extended the results in [19] to equations with a middle term. ...
- Citing Article
March 1983
Czechoslovak Mathematical Journal