Necessary and sufficient conditions for oscillation of second-order delay differential equations: Applied Mathematics ´19

Year, pages: 2020, 135 - 146

In this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form\vadjust{\vskip-1.0ex} \[ (r(x^\prime)^γ)^\prime(t)+ q(t)x^α(τ(t))=0 . \] Under the assumption $\int^∞(r(η))^-1/γ \textup{d} η=∞$, we consider the two cases when $γ ≥ α$ and $γ ≤ α$. Further, some illustrative examples showing applicability of the new results are included, and state an open problem.

Santra, S. 2020. Necessary and sufficient conditions for oscillation of second-order delay differential equations: Applied Mathematics ´19. In Tatra Mountains Mathematical Publications, vol. 75, no.1, pp. 135-146. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0009

Santra, S. (2020). Necessary and sufficient conditions for oscillation of second-order delay differential equations: Applied Mathematics ´19. Tatra Mountains Mathematical Publications, 75(1), 135-146. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0009

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

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