Currently displaying 1 – 20 of 36

Showing per page

Order by Relevance | Title | Year of publication

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 .

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.

Singular eigenvalue problems for second order linear ordinary differential equations

Árpád ElbertTakaŝi KusanoManabu Naito — 1998

Archivum Mathematicum

We consider linear differential equations of the form ( p ( t ) x ' ) ' + λ q ( t ) x = 0 ( p ( t ) > 0 , q ( t ) > 0 ) ( A ) on an infinite interval [ a , ) and study the problem of finding those values of λ for which () has principal solutions x 0 ( t ; λ ) vanishing at t = a . This problem may well be called a singular eigenvalue problem, since requiring x 0 ( t ; λ ) to be a principal solution can be considered as a boundary condition at t = . Similarly to the regular eigenvalue problems for () on compact intervals, we can prove a theorem asserting that there exists a sequence { λ n } of eigenvalues such...

Page 1 Next

Download Results (CSV)