Results 11 to 20 of about 60 (57)
Euler Type Half‐Linear Differential Equation with Periodic Coefficients
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We investigate oscillatory properties of the perturbed half‐linear Euler differential equation. We show that the results of the recent paper by O. Došlý and H. Funková (2012) remain to hold when constants in perturbation terms are replaced by periodic functions.
Ondřej Došlý +2 more
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Convergent Disfocality and Nondisfocality Criteria for Second‐Order Linear Differential Equations
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 This paper presents a method to determine whether the second‐order linear differential equation y′′ + q(x)y = 0 is either disfocal or nondisfocal in a fixed interval. The method is based on the recursive application of a linear operator to certain functions and yields upper and lower bounds for the distances between a zero and its adjacent critical ...
Pedro Almenar +2 more
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Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients
Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 We investigate a type of the Sturm‐Liouville difference equations with almost periodic coefficients. We prove that there exists a constant, which is the borderline between the oscillation and the nonoscillation of these equations. We compute this oscillation constant explicitly.
Petr Hasil +2 more
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On Constants in Nonoscillation Criteria for Half‐Linear Differential Equations
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 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. 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 +2 more
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Sturmian comparison theorem for hyperbolic equations on a rectangular prism
AIMS Mathematics<abstract><p>In this paper, new Sturmian comparison results were obtained for linear and nonlinear hyperbolic equations on a rectangular prism. The results obtained for linear equations extended those given by Kreith [Sturmian theorems on hyperbolic equations, <italic>Proc. Amer. Math. Soc.</italic>, <bold>22</bold> (
Ozbekler, Abdullah +2 more
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Weyl‐Titchmarsh Theory for Time Scale Symplectic Systems on Half Line
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 We develop the Weyl‐Titchmarsh theory for time scale symplectic systems. We introduce the M(λ)‐function, study its properties, construct the corresponding Weyl disk and Weyl circle, and establish their geometric structure including the formulas for their center and matrix radii. Similar properties are then derived for the limiting Weyl disk. We discuss
Roman Šimon Hilscher +2 more
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Sturmian comparison theorems for three-term recurrence equations
Journal of Mathematical Analysis and Applications, 1985 The author considers a discrete analogue of an ordinary, regular, self- adjoint second-order differential equation. For these homogeneous difference equations (or recurrences) with homogeneous discrete boundary conditions of Sturm-Liouville type, several comparison theorems concerning the existence and inclusion of nodes of the corresponding non ...
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International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We obtain the asymptotic distribution of the nonprincipal eigenvalues associated with the singular problem x″ + λq(t)x = 0 on an infinite interval [a, +∞). Similar to the regular eigenvalue problem on compact intervals, we can prove a Weyl‐type expansion of the eigenvalue counting function, and we derive the asymptotic behavior of the eigenvalues.
Juan Pablo Pinasco
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Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation
Abstract and Applied Analysis, Volume 2004, Issue 4, Page 285-294, 2004., 2004 We present basic methods of oscillation theory of symplectic difference systems (SDSs). A particular attention is devoted to the variational principle and to the transformation method. Hyperbolic Prüfer transformation for SDSs is established.
Ondřej Došlý
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On certain comparison theorems for half‐linear dynamic equations on time scales
Abstract and Applied Analysis, Volume 2004, Issue 7, Page 551-565, 2004., 2004 We obtain comparison theorems for the second‐order half‐linear dynamic equation [r(t)Φ(yΔ)]Δ+p(t)Φ(yσ)=0, where Φ(x) = |x|α−1sgn x with α > 1. In particular, it is shown that the nonoscillation of the previous dynamic equation is preserved if we multiply the coefficient p(t) by a suitable function q(t) and lower the exponent α in the nonlinearity Φ ...
Pavel Řehák
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