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Picone's Identity for Ordinary Differential Operators of Even Order

Takasi KusanoNorio Yoshida — 1975

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

In questo lavoro la ben nota identità di M. Picone è generalizzata agli operatori differenziali ordinari autoaggiunti di ordine superiore. Tale identità generalizzata è impiegata per conseguire teoremi di confronto del tipo di Sturm e criteri di non oscillazione per le soluzioni di equazioni (o diseguaglianze) relative a tali operatori.

Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type

Takaŝi KusanoPavol Marušiak — 2000

Mathematica Bohemica

This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasilinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as t .

Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order

Jaroslav JarošTakaŝi KusanoN. Yoshida — 2002

Archivum Mathematicum

In the paper a comparison theory of Sturm-Picone type is developed for the pair of nonlinear second-order ordinary differential equations first of which is the quasilinear differential equation with an oscillatory forcing term and the second is the so-called half-linear differential equation. Use is made of a new nonlinear version of the Picone’s formula.

An oscillatory half-linear differential equation

Árpád ElbertTakaŝi KusanoTomoyuki Tanigawa — 1997

Archivum Mathematicum

A second-order half-linear ordinary differential equation of the type ( | y ' | α - 1 y ' ) ' + α q ( t ) | y | α - 1 y = 0 ( 1 ) is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.

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