Second-order half-linear delay differential equations: Oscillation tests

Yıl 2020, , 385 - 393, 30.12.2020

O. Bazighifan , Shyam Sundar Santra

https://doi.org/10.31197/atnaa.751034

Öz

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 $
\bigl(r(y^{\prime})^\gamma\bigr)^{\prime}(t)+ q(t)y^\alpha(\tau(t))=0\,.$
We study this equation under the assumption $\int^{\infty}\big(r(\eta)\big)^{-1/\gamma} d\eta=\infty$ and consider two cases when $\gamma > \alpha$ and $\gamma < \alpha$. We provide examples, illustrating the results and state an open problem.

Anahtar Kelimeler

Oscillation, nonoscillation, delay, half-linear, Lebesgue's dominated convergence theorem

Kaynakça

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