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On the oscillation of a class of linear homogeneous third order differential equations

N. Parhi, P. Das (1998)

Archivum Mathematicum

In this paper we have considered completely the equation y ' ' ' + a ( t ) y ' ' + b ( t ) y ' + c ( t ) y = 0 , ( * ) where a ∈ C 2 ( [ σ , ∞ ) , R ) , b ∈ C 1 ( [ σ , ∞ ) , R ) , c ∈ C ( [ σ , ∞ ) , R ) and σ ∈ R such that a ( t ) ≤ 0 , b ( t ) ≤ 0 and c ( t ) ≤ 0 . It has been shown that the set of all oscillatory solutions of (*) forms a two-dimensional subspace of the solution space of (*) provided that (*) has an oscillatory solution. This answers a question raised by S. Ahmad and A.  C. Lazer earlier.

On the oscillatory integration of some ordinary differential equations

Octavian G. Mustafa (2008)

Archivum Mathematicum

Conditions are given for a class of nonlinear ordinary differential equations x ' ' + a ( t ) w ( x ) = 0 , t ≥ t 0 ≥ 1 , which includes the linear equation to possess solutions x ( t ) with prescribed oblique asymptote that have an oscillatory pseudo-wronskian x ' ( t ) - x ( t ) t .

On the rate of convergence to the neutral attractor of a family of one-dimensional maps

T. Nowicki, M. Sviridenko, G. Świrszcz, S. Winograd (2009)

Fundamenta Mathematicae

For a family of maps f d ( p ) = 1 - ( 1 - p / d ) d , d ∈ [2,∞], p ∈ [0,1]. we analyze the speed of convergence (including constants) to the globally attracting neutral fixed point p = 0. The study is motivated by a problem in the optimization of routing. The aim of this paper is twofold: (1) to extend the usage of dynamical systems to unexplored areas of algorithms and (2) to provide a toolbox for a precise analysis of the iterates near a non-degenerate neutral fixed point.

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