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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Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations [PDF]
Abstract and Applied Analysis, 2011 We study perturbations of the nonoscillatory half-linear differential equation (r(t)Φ(x'))'+c(t)Φ(x)=0, Φ(x):=|x|p-2x, p>1. We find explicit formulas for the functions r̂, ĉ such that the equation [(r(t)+λr̂(t))Φ(x')]'+[c(t)+μĉ(t)]Φ(x)=0 is ...
Ondřej Došlý, Simona Fišnarová
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Oscillation of Half-Linear Differential Equations with Delay [PDF]
Abstract and Applied Analysis, 2013 We study the half-linear delay differential equation , , We establish a new a priori bound for the nonoscillatory solution of this equation and utilize this bound to derive new oscillation criteria for this equation in terms of oscillation criteria for ...
Simona Fišnarová, Robert Mařík
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Oscillation and non-oscillation criterion for Riemann–Weber type half-linear differential equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2016 By the combination of the modified half-linear Prüfer method and the Riccati technique, we study oscillatory properties of half-linear differential equations.
Petr Hasil, Michal Veselý
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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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On Constants in Nonoscillation Criteria for Half-Linear Differential Equations [PDF]
Abstract and Applied Analysis, 2011 We study the half-linear differential equation (r(t)Φ(x′))′+c(t)Φ(x)=0, where Φ(x)=|x|p−2x, p>1. Using the modified Riccati technique, we derive new nonoscillation criteria for this equation.
Simona Fišnarová, Robert Mařík
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Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations [PDF]
Abstract and Applied Analysis, 2011 We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear q-difference equation Dq(Φ(Dqy(t)))+p(t)Φ(y(qt))=0, t∈{qk:k∈N0} with q>1, Φ(u)=|u|α−1sgnu with α>1, to behave like
Pavel Řehák
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Nonoscillatory half-linear difference equations and recessive solutions
Advances in Difference Equations, 2005 Recessive and dominant solutions for the nonoscillatory half-linear difference equation are investigated. By using a uniqueness result for the zero-convergent solutions satisfying a suitable final condition, we prove that recessive solutions are the ...
Došlá Zuzana +2 more
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Nonoscillation of higher order half-linear differential equations
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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