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

Czechoslovak Mathematical Journal (2000)

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

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topDošlý, 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 -

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## Citations in EuDML Documents

top- Ondřej Došlý, The Picone identity for a class of partial differential equations
- Ondřej Došlý, Qualitative theory of half-linear second order differential equations
- Ondřej Došlý, Oscillation Theory of Linear Difference Equations
- Ondřej Došlý, Jaroslav Jaroš, A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations

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