A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations

Ondřej Došlý; Jaroslav Jaroš

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 4, page 335-345
  • ISSN: 0044-8753

Abstract

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We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations ( r ( t ) | x ' | α - 2 x ' ) ' + c ( t ) | x | β - 2 x = f ( t ) , 1 < α ≤ β , t ∈ I = ( a , b ) , ( * ) where the endpoints a , b of the interval I are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested.

How to cite

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Došlý, Ondřej, and Jaroš, Jaroslav. "A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations." Archivum Mathematicum 039.4 (2003): 335-345. <http://eudml.org/doc/249136>.

@article{Došlý2003,
abstract = {We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations \[ (r(t)|x^\{\prime \}|^\{\alpha -2\}x^\{\prime \})^\{\prime \}+c(t)|x|^\{\beta -2\}x=f(t)\,,\quad 1<\alpha \le \beta ,\ t\in I=(a,b)\,, \qquad \mathrm \{(*)\}\] where the endpoints $a$, $b$ of the interval $I$ are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested.},
author = {Došlý, Ondřej, Jaroš, Jaroslav},
journal = {Archivum Mathematicum},
keywords = {Picone’s identity; forced quasilinear equation; principal solution; Picone's identity; principal solution},
language = {eng},
number = {4},
pages = {335-345},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations},
url = {http://eudml.org/doc/249136},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Došlý, Ondřej
AU - Jaroš, Jaroslav
TI - A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 4
SP - 335
EP - 345
AB - We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations \[ (r(t)|x^{\prime }|^{\alpha -2}x^{\prime })^{\prime }+c(t)|x|^{\beta -2}x=f(t)\,,\quad 1<\alpha \le \beta ,\ t\in I=(a,b)\,, \qquad \mathrm {(*)}\] where the endpoints $a$, $b$ of the interval $I$ are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested.
LA - eng
KW - Picone’s identity; forced quasilinear equation; principal solution; Picone's identity; principal solution
UR - http://eudml.org/doc/249136
ER -

References

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