Improved oscillation results for second-order half-linear delay differential equations

Yıl 2019, Cilt: 48 Sayı: 1, 170 - 179, 01.02.2019

George E. Chatzarakis İrena Jadlovska

Öz

 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.

Anahtar Kelimeler

half-linear differential equation, delay, second-order, oscillation

Kaynakça

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