Necessary and sufficient conditions for oscillatory and asymptotic behaviour of solutions to second-order nonlinear neutral differential equations with several delays: Applied Mathematics ´19

Rok, strany: 2020, 121 - 134

In this paper, necessary and sufficient conditions are obtained for oscillatory and asymptotic behavior of solutions to second-order nonlinear neutral delay differential equations of the form \begin{equation} ((\dd) / (\dt))\Bgr[r(t)\bgl[((\dd) / (\dt))\bl(x(t)+p(t)x(t-τ)\br)\bgr]^α\Bgr] +∑_i=1^mq_i(t)H\bl(x(t-σ_i)\br)=0  for t≥{}t₀>0,\notag \end{equation} under the assumption $\int^∞\big(r(η)\big)^-1/α\ddη=∞$. Our main tool is Lebesque's dominated convergence theorem. Further, some illustrative examples showing the applicability of the new results are included.

ISO 690:

Santra, S. 2020. Necessary and sufficient conditions for oscillatory and asymptotic behaviour of solutions to second-order nonlinear neutral differential equations with several delays: Applied Mathematics ´19. In Tatra Mountains Mathematical Publications, vol. 75, no.1, pp. 121-134. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0008

APA:

Santra, S. (2020). Necessary and sufficient conditions for oscillatory and asymptotic behaviour of solutions to second-order nonlinear neutral differential equations with several delays: Applied Mathematics ´19. Tatra Mountains Mathematical Publications, 75(1), 121-134. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0008

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

Licensed under the Creative Commons Attribution-NC-ND4.0 International Public License.