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The main purpose of this paper is to improve recent oscillation results for the second-order half-linear delay differential equation \[\left(r(t)\left(y'(t)\right)^\gamma\right)'+q(t)y^\gamma(\tau(t))= 0, \quad t\geq t_0,\] under the condition \[\int_{t_0}^{\infty}\frac{\text{d} t}{r^{1/\gamma}(t)} \lt… Click to show full abstract
The main purpose of this paper is to improve recent oscillation results for the second-order half-linear delay differential equation \[\left(r(t)\left(y'(t)\right)^\gamma\right)'+q(t)y^\gamma(\tau(t))= 0, \quad t\geq t_0,\] under the condition \[\int_{t_0}^{\infty}\frac{\text{d} t}{r^{1/\gamma}(t)} \lt \infty.\] Our approach is essentially based on establishing sharper estimates for positive solutions of the studied equation than those used in known works. Two examples illustrating the results are given.
Journal Title: Opuscula Mathematica
Year Published: 2019
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