Results 1 to 10 of about 94 (85)
Comparison results for two-dimensional half-linear cyclic differential systems [PDF]
, 2017 summary:Two identities of the Picone type for a class of half-linear differential systems in the plane are established and the Sturmian comparison theory for such systems is developed with the help of these new ...
Kusano Takaŝi +3 more
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International Journal of Differential Equations, Volume 2017, Issue 1, 2017., 2017 We compute explicitly the oscillation constant for Euler type half‐linear second‐order differential equation having multi‐different periodic coefficients.
Adil Misir +2 more
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Solvability of Nth Order Linear Boundary Value Problems
International Journal of Differential Equations, Volume 2015, Issue 1, 2015., 2015 This paper presents a method that provides necessary and sufficient conditions for the existence of solutions of nth order linear boundary value problems. The method is based on the recursive application of a linear integral operator to some functions and the comparison of the result with these same functions.
P. Almenar, L. Jódar, Peiguang Wang
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Conditional Oscillation of Half‐Linear Differential Equations with Coefficients Having Mean Values
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We prove that the existence of the mean values of coefficients is sufficient for second‐order half‐linear Euler‐type differential equations to be conditionally oscillatory. We explicitly find an oscillation constant even for the considered equations whose coefficients can change sign.
Petr Hasil +3 more
wiley +1 more source
Oscillation of Half‐Linear Differential Equations with Delay
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We study the half‐linear delay differential equation (r(t)Φ(x′(t)))′ + c(t)Φ(x(τ(t))) = 0, Φ(x): = |x|p−2x, p > 1. 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 ...
Simona Fišnarová +2 more
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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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