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Generalized discrete Riccati equation and oscillation of half-linear difference equations
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Pavel Rehak
exaly +3 more sources
Perturbations of the half-linear Euler–Weber type differential equation
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Ondřej Došlý
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Summation inequalities and half-linear difference equations
The aim of this paper is to present new summation inequalities and to shaw that the half-linear difference equation ... exhibits not only similarities but also some discrepancies with the linear case, especially as regards the possible coexistence of the so-called extremal solutions. Some of our results are new also for the linear difference equation.
Zuzana Došlá +2 more
exaly +6 more sources
Oscillation of Half-Linear Differential Equations with Delay [PDF]
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 an ordinary half-linear differential equation.
Simona Fišnarová, Robert Mařík
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Asymptotic properties for half-linear difference equations [PDF]
Summary: Asymptotic properties of the half-linear difference equation \[ \Delta (a_{n}| \Delta x_{n}| ^{\alpha }\text{sgn}\, \Delta x_{n} )=b_{n}| x_{n+1}| ^{\alpha }\text{sgn}\, x_{n+1} \tag{\(*\)} \] are investigated by means of some summation criteria.
M. CECCHI +3 more
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On Constants in Nonoscillation Criteria for Half‐Linear Differential Equations [PDF]
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. The results are closely related to the classical Hille‐Nehari criteria and allow to replace the fixed constants in known nonoscillation criteria by a ...
Simona Fišnarová, Robert Mařík
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Nonoscillation of half-linear dynamic equations
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Serena Matucci, Pavel Rehák
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ON CONNECTED HALF-LINEAR DIFFERENTIAL EQUATIONS
Summary: Relations among several classes of half-linear differential equations with or without delays are established. By means of these connections, the existence of eventually positive solutions can be inferred from the properties of either one of these families of equations.
Zhang, Guang, Cheng, Sui Sun
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Half-linear differential equations with oscillating coefficient
n ...
M. CECCHI, Z. DOSLA, MARINI, MAURO
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Two‐Parametric Conditionally Oscillatory Half‐Linear Differential Equations [PDF]
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 , such that the equation is conditionally oscillatory, that is, there exists a constant γ such that the previous equation is oscillatory if μ − λ > γ and nonoscillatory ...
Došlý, Ondřej, Fišnarová, Simona
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