Oscillation of second order nonlinear differential equation with sub-linear neutral term

Abstract

Abstract. In this paper the authors established sufficient conditions for the oscillation of all solutions of a nonlinear differential equationwhere α and β are ratio of odd positive integers. The results obtained here extend and improve some of the existing results. Examples are included to illustrate the importance of the results.Mathematics subject classification (2010): 34C10, 34K11.

Oscillatory criteria for second order differential equations with several sublinear neutral terms

“…The aim of this paper is to fulfil this gap in oscillation theory and to introduce new oscillatory criteria for such equations. Presented results generalize those of Tamilvanan et al [20], where the second order differential equation with only one sublinear neutral term has been investigated. The results obtained are applicable also for non-neutral differential equations (p i (t) ≡ 0).…”

“…However, there are only few results dealing with the oscillation of second order differential equations with sublinear neutral terms [2,8,20]. The aim of this paper is to fulfil this gap in oscillation theory and to introduce new oscillatory criteria for such equations.…”

Oscillatory behavior of second order delay dynamic equations with a sub-linear neutral term on time scales

“…However, it seems that there are no known results for the oscillation of second-order dynamic equations with positive sublinear neutral terms. Also, in special cases T = R and T = Z there are a few literature present sufficient criteria for the oscillatory behavior of second-order differential equations and difference equations with positive sublinear neutral terms, see; [1,4,6,[12][13][14][15][16]25].…”

Oscillation of second order nonlinear difference equations with super-linear neutral term

“…In view of the above observations our aim in this paper is to present some new sufficient conditions which ensure that all solutions of equation (1.1) when the condition (1.3) holds and our results are different from that of [7,9]. For related results concerning second order differential equations with sublinear or superlinear neutral terms, we refer the reader to [3,8,13,14].…”