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An integral condition of oscillation for equation y ' ' ' + p ( t ) y ' + q ( t ) y = 0 with nonnegative coefficients

Anton Škerlík (1995)

Archivum Mathematicum

Our aim in this paper is to obtain a new oscillation criterion for equation y ' ' ' + p ( t ) y ' + q ( t ) y = 0 with a nonnegative coefficients which extends and improves some oscillation criteria for this equation. In the special case of equation (*), namely, for equation y ' ' ' + q ( t ) y = 0 , our results solve the open question of C h a n t u r i y a .

An oscillatory half-linear differential equation

Árpád Elbert, Takaŝi Kusano, Tomoyuki 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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