J 2012

On certain asymptotic class of solutions to second order linear q-difference equations

ŘEHÁK, Pavel

Basic information

Original name

On certain asymptotic class of solutions to second order linear q-difference equations

Authors

ŘEHÁK, Pavel (203 Czech Republic, guarantor, belonging to the institution)

Edition

Journal of Physics A: Mathematical and Theoretical, Velká Británie, IOP Publishing, 2012, 1751-8113

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 1.766

RIV identification code

RIV/00216224:14410/12:00057291

Organization unit

Faculty of Education

DOI

UT WoS

000300259500007

Keywords in English

q-difference equation; asymptotic behavior; regular variation; oscillation
Změněno: 22/4/2013 13:28, Dana Nesnídalová

Abstract

V originále

The paper deals with the linear second order $q$-difference equation $y(q^2t)+a(t)y(qt)+b(t)y(t)=0$, $b(t)\ne 0$, considered on $\{q^k:k\in\N_0\}$, $q>1$. The class of functions satisfying the relation $y(qt)/y(t)\sim\omega(t)$ as $t\to\infty$ for some function $\omega$ is introduced and studied. Sufficient and necessary conditions are established for the equation to have solutions in this class. Related results concerning estimates for solutions and (non)oscillation of all solutions are discussed. A comparison with existing results is made and some applications are given.

Links

GAP201/10/1032, research and development project
Name: Diferenční rovnice a dynamické rovnice na ,,time scales'' III (Acronym: Difrov)
Investor: Czech Science Foundation