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1
Content available Kneser-type oscillation criteria for second-order half-linear advanced difference equations
Indrajith N., Graef John R., Thandapani E.
Opuscula Mathematica
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2022
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Vol. 42, no. 1
55--64
EN
The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.
2
Content available Oscillation criteria for even order neutral difference equations
Selvarangam S., Rupadevi S. A., Thandapani E., Pinelas S.
Opuscula Mathematica
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2019
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Vol. 39, no. 1
91--108
EN
In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form [formula] where m ≥ 2 is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results.
3
Content available Oscillation of second order difference equation with a sub-linear neutral term
Dharuman C., Graef J. R., Thandapani E., Vidhyaa K. S.
Journal of Mathematics and Applications
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2017
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Vol. 40
59--67
EN
This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.
4
Content available remote Improved oscillation criteria for second order nonlinear delay difference equations with non-positive neutral term
Thandapani E., Selvarangam S., Rama R., Madhan M.
Fasciculi Mathematici
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2016
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Nr 56
155--165
EN
In this paper, we present some oscillation criteria for second order nonlinear delay difference equation with non-positive neutral term of the form ∆(an (∆zn )α )+qn f(xn-σ) )=0, n>no >0, where zn - xn - pn xn-r, and α is a ratio of odd positive integers. Examples are provided to illustrate the results. The results obtained in this paper improve and complement to some of the existing results.
5
Content available remote Oscillation of higher-order half-linear neutral differential equations
Tang S., Li T., Thandapani E.
Demonstratio Mathematica
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2013
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Vol. 46, nr 1
101--109
EN
In this paper, we establish some new oscillation criteria for the higher-order half-linear neutral differential equation (…). An example is given to illustrate the main results.
6
Content available remote Oscillations of fourth order quasilinear difference equations
Thandapani E., Selvaraj B.
Fasciculi Mathematici
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2007
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Nr 37
109-119
EN
Consider the fourth order quasilinear difference equation of the form where {pn} is a positive sequence and {qn} is a sequence of non-negative reals, a and ,3 are ratios of odd positive integers. We obtain some new sufficient conditions for the oscillation of all solutions of equation (*). Examples are inserted to illustrate the importance of our results.
7
Content available remote Oscillatory properties of third order neutral delay difference equations
Thandapani E., Mahalingam K.
Demonstratio Mathematica
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2002
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Vol. 35, nr 2
325-337
EN
Some new sufficient criteria for the oscillation of all solutions of the neutral difference equation are obtained. Existence of nonoscillatory solution and its asymptotic behavior are also discussed. Examples illustrating the results are inserted.
8
Content available remote Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations
Graef J. R., Thandapani E.
Fasciculi Mathematici
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2001
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Nr 31
23-36
EN
The authors consider the nonlinear difference equation (E) delta2 ((delta(bn delta yn))+f(n,yn-t)=0, n należy N(no)={no,no+1,...}, here {an} and {bn} are positive real sequences, I is a nonnegative integer, f: N(no) x R R is a continuous function with uf(n, u) > 0 for all u nierówne 0. They obtain necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior. They also obtain sufficient conditions for all solutions to be oscillatory if/ is either strongly sublinear or strongly superlinear. Examples of their results are also included.
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