Modified Riccati technique for half-linear differential equations with delay [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2014 We study the half-linear differential equation $$ (r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1. $$ We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear ...
Simona Fišnarová, Robert Marik
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Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2008 This paper is concerned with the oscillatory behavior of the fourth-order nonlinear differential equation $$ \bigl(p(t)|x^{\prime\prime}|^{\alpha-1}\,x^{\prime\prime}\bigr)^{\prime\prime} +q(t)|x|^{\beta-1}x=0\,,\tag{E} $$ where $\alpha>0$, $\beta>0$ are
Jelena Manojlović, J. Milosevic
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Nonoscillation of higher order half-linear differential equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2015 We establish nonoscillation criteria for even order half-linear differential equations. The principal tool we use is the Wirtinger type inequality combined with various perturbation techniques.
Ondrej Dosly, Vojtěch Růžička
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Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order
Mathematics, 2023 In this paper, we find new oscillation criteria for second-order advanced functional half-linear differential equations. Our results extend and improve recent criteria for the same equations established previously by several authors and cover the ...
Taher S. Hassan +2 more
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Oscillation criteria for perturbed half-linear differential equations
Electronic Journal of Qualitative Theory of Differential EquationsOscillatory properties of perturbed half-linear differential equations are investigated. We make use of the modified Riccati technique. A certain linear differential equation associated with the modified Riccati equation plays an important part. Improved
Manabu Naito
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Oscillation result for half-linear delay difference equations of second-order
Mathematical Biosciences and Engineering, 2022 In this paper, we obtain the new single-condition criteria for the oscillation of second-order half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results.
Chinnasamy Jayakumar +6 more
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Non-oscillation of half-linear differential equations with periodic coefficients [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2015 We consider half-linear Euler type differential equations with general periodic coefficients. It is well-known that these equations are conditionally oscillatory, i.e., there exists a border value given by their coefficients which separates oscillatory ...
Petr Hasil, Michal Veselý
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Oscillation of half-linear differential equations with mixed type of argument
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper is devoted to the study of the oscillatory behavior of half-linear functional differential equations with deviating argument of the form \begin{equation*}\label{Eabs} \left(r(t)(y'(t))^{\alpha}\right)'=p(t)y^{\alpha}(\tau(t)). \tag{$E$} \end{
Jozef Džurina, Blanka Baculíková
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Oscillation and nonoscillation of two terms linear and half-linear equations of higher order
Electronic Journal of Qualitative Theory of Differential Equations, 2010 In this paper we investigate the properties of nonoscillation for the equation $$(-1)^{n}(\rho(t)|y^{(n)}|^{p-2}y^{(n)})^{(n)}-v(t)|y|^{p-2}y=0,$$ where ...
Ryskul. Oinarov, S. Y. Rakhimova
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New Oscillation Results For Third-Order Half-Linear Neutral Differential Equations
Mathematics, 2020 The main purpose of this paper is to obtain criteria for the oscillation of all solutions of a third-order half-linear neutral differential equation.
K. S. Vidhyaa +2 more
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