Local analysis of nonstandard functions of pre-distributional type
V. Komkov, T. G. McLaughlin (1984)
Annales Polonici Mathematici
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V. Komkov, T. G. McLaughlin (1984)
Annales Polonici Mathematici
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Anna Andruch-Sobiło, Andrzej Drozdowicz (2008)
Mathematica Bohemica
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In the paper we consider the difference equation of neutral type where ; , is strictly increasing and is nondecreasing and , , . We examine the following two cases: and where , are positive integers. We obtain sufficient conditions under which all nonoscillatory solutions of the above equation tend to zero as with a weaker assumption on than the usual assumption that is used in literature.
Yeter Ş. Yilmaz, Ağacik Zafer (2001)
Czechoslovak Mathematical Journal
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The paper is concerned with oscillation properties of -th order neutral differential equations of the form where is a real number with , , , with and . Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations...
George E. Chatzarakis, Deepalakshmi Rajasekar, Saravanan Sivagandhi, Ethiraju Thandapani (2024)
Mathematica Bohemica
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We study the oscillatory behavior of the second-order quasi-linear retarded difference equation under the condition (i.e., the noncanonical form). Unlike most existing results, the oscillatory behavior of this equation is attained by transforming it into an equation in the canonical form. Examples are provided to show the importance of our main results.
Ján Ohriska (1998)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We consider the second order self-adjoint differential equation (1) (r(t)y’(t))’ + p(t)y(t) = 0 on an interval I, where r, p are continuous functions and r is positive on I. The aim of this paper is to show one possibility to write equation (1) in the same form but with positive coefficients, say r₁, p₁ and to derive a sufficient condition for equation (1) to be oscillatory in the case p is nonnegative and converges.
Baoguo Jia (2010)
Annales Polonici Mathematici
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Consider the third order nonlinear dynamic equation , (*) on a time scale which is unbounded above. The function f ∈ C(,) is assumed to satisfy xf(x) > 0 for x ≠ 0 and be nondecreasing. We study the oscillatory behaviour of solutions of (*). As an application, we find that the nonlinear difference equation , where α ≥ -1, γ > 0, c > 3, is oscillatory.
Said R. Grace (1999)
Czechoslovak Mathematical Journal
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Sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations to be oscillatory, where , , . Also, we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations where , and are real constants and .
Anna Andruch-Sobiło, Małgorzata Migda (2005)
Mathematica Bohemica
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In this note we consider the third order linear difference equations of neutral type where , , We examine the following two cases: where , are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory.