- Hacettepe Journal of Mathematics and Statistics
- Vol: 48 Issue: 1
- Improved oscillation results for second-order half-linear delay differential equations
Improved oscillation results for second-order half-linear delay differential equations
Authors : George E. Chatzarakis, Irena Jadlovska
Pages : 170-179
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Publication Date : 2019-02-01
Article Type : Research
Abstract : In this paper, we study the second-order half-linear delay differential equation of the form \[(r(t)(y'(t))^\alpha)'+q(t)y^\alpha(\tau(t))= 0.\:\:\:(E)\] We establish new oscillation criteria for (E), which improve a number of related ones in the literature. Our approach essentially involves establishing sharper estimates for the positive solutions of (E) than those presented in known works and a comparison principle with first-order delay differential inequalities. We illustrate the improvement over the known results by applying and comparing our method with the other known methods on the particular example of Euler-type equations.Keywords : half-linear differential equation, delay, second-order, oscillation