Methods of oscillation theory of half-linear second order differential equations

Ondřej Došlý

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 3, page 657-671
  • ISSN: 0011-4642

Abstract

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In this paper we investigate oscillatory properties of the second order half-linear equation ( r ( t ) Φ ( y ' ) ) ' + c ( t ) Φ ( y ) = 0 , Φ ( s ) : = | s | p - 2 s . ( * ) Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.

How to cite

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Došlý, Ondřej. "Methods of oscillation theory of half-linear second order differential equations." Czechoslovak Mathematical Journal 50.3 (2000): 657-671. <http://eudml.org/doc/30592>.

@article{Došlý2000,
abstract = {In this paper we investigate oscillatory properties of the second order half-linear equation \[ (r(t)\Phi (y^\{\prime \}))^\{\prime \}+c(t)\Phi (y)=0, \quad \Phi (s):= |s|^\{p-2\}s. \qquad \mathrm \{\{(*)\}\}\] Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.},
author = {Došlý, Ondřej},
journal = {Czechoslovak Mathematical Journal},
keywords = {half-linear equation; Riccati technique; variational principle; reciprocity principle; principal solution; oscillation and nonoscillation criteria; half-linear equation; Riccati technique; variational principle; reciprocity principle; principal solution; oscillation and nonoscillation criteria},
language = {eng},
number = {3},
pages = {657-671},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Methods of oscillation theory of half-linear second order differential equations},
url = {http://eudml.org/doc/30592},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Došlý, Ondřej
TI - Methods of oscillation theory of half-linear second order differential equations
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 657
EP - 671
AB - In this paper we investigate oscillatory properties of the second order half-linear equation \[ (r(t)\Phi (y^{\prime }))^{\prime }+c(t)\Phi (y)=0, \quad \Phi (s):= |s|^{p-2}s. \qquad \mathrm {{(*)}}\] Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.
LA - eng
KW - half-linear equation; Riccati technique; variational principle; reciprocity principle; principal solution; oscillation and nonoscillation criteria; half-linear equation; Riccati technique; variational principle; reciprocity principle; principal solution; oscillation and nonoscillation criteria
UR - http://eudml.org/doc/30592
ER -

References

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