- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 4
- Second-order half-linear delay differential equations: Oscillation tests
Second-order half-linear delay differential equations: Oscillation tests
Authors : O. Bazighifan, Shyam Sundar Santra
Pages : 385-393
Doi:10.31197/atnaa.751034
View : 4 | Download : 2
Publication Date : 2020-12-30
Article Type : Research
Abstract :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.Keywords : Oscillation, nonoscillation, delay, half-linear, Lebesgue's dominated convergence theorem