Detail publikace

A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient

Originální název

A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient

Anglický název

A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient

Jazyk

en

Originální abstrakt

A linear $(k+1)$th-order discrete delayed equation $\Delta x(n)=-p(n)x(n-k)$ where $p(n)$ is a positive sequence is considered for $n\to\infty$. This equation is known to have a positive solution if the sequence $p(n)$ satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for $p(n)$, all solutions of the equation considered are oscillating for $n\to\infty$.

Anglický abstrakt

A linear $(k+1)$th-order discrete delayed equation $\Delta x(n)=-p(n)x(n-k)$ where $p(n)$ is a positive sequence is considered for $n\to\infty$. This equation is known to have a positive solution if the sequence $p(n)$ satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for $p(n)$, all solutions of the equation considered are oscillating for $n\to\infty$.

BibTex


@article{BUT73392,
  author="Jaromír {Baštinec} and Leonid {Berezansky} and Josef {Diblík} and Zdeněk {Šmarda}",
  title="A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient",
  annote="A linear $(k+1)$th-order discrete delayed equation $\Delta x(n)=-p(n)x(n-k)$ where $p(n)$ is a positive sequence is considered for $n\to\infty$. This equation is known to have a positive solution if the sequence $p(n)$ satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for $p(n)$,  all solutions of the equation considered are oscillating for $n\to\infty$.",
  chapter="73392",
  number="Article ID 58632",
  volume="vol. 2011,",
  year="2011",
  month="august",
  pages="1--28",
  type="journal article - other"
}