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Article

Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations

1
Department of Mathematics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 760 05 Zlín, Czech Republic
2
Department of Mathematics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic
*
Author to whom correspondence should be addressed.
Academic Editor: Jozef Džurina
Mathematics 2021, 9(3), 235; https://doi.org/10.3390/math9030235
Received: 28 December 2020 / Revised: 18 January 2021 / Accepted: 20 January 2021 / Published: 25 January 2021
(This article belongs to the Special Issue Oscillation Theory for Differential Equations)
We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equation is ensured by the divergence of a certain integral. The second one provides the condition of the oscillation in the case where the relevant integral converges, and it can be seen as a Hille–Nehari-type criterion. The use of the results is shown in several examples, in which the Euler-type equation and its perturbations are considered. View Full-Text
Keywords: half-linear neutral differential equation; oscillation criteria; modified Riccati technique half-linear neutral differential equation; oscillation criteria; modified Riccati technique
MDPI and ACS Style

Pátíková, Z.; Fišnarová, S. Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations. Mathematics 2021, 9, 235. https://doi.org/10.3390/math9030235

AMA Style

Pátíková Z, Fišnarová S. Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations. Mathematics. 2021; 9(3):235. https://doi.org/10.3390/math9030235

Chicago/Turabian Style

Pátíková, Zuzana, and Simona Fišnarová. 2021. "Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations" Mathematics 9, no. 3: 235. https://doi.org/10.3390/math9030235

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