Some oscillation theorems for second order differential equations

Chung-Fen Lee; Cheh Chih Yeh; Chuen-Yu Gau

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 845-861
  • ISSN: 0011-4642

Abstract

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In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation ( r ( t ) Φ ( u ' ( t ) ) ) ' + c ( t ) Φ ( u ( t ) ) = 0 , where (i) r , c ∈ C ( [ t 0 , ∞ ) , ℝ : = ( - ∞ , ∞ ) ) and r ( t ) > 0 on [ t 0 , ∞ ) for some t 0 ≥ 0 ; (ii) Φ ( u ) = | u | p - 2 u for some fixed number p > 1 . We also generalize some results of Hille-Wintner, Leighton and Willet.

How to cite

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Lee, Chung-Fen, Yeh, Cheh Chih, and Gau, Chuen-Yu. "Some oscillation theorems for second order differential equations." Czechoslovak Mathematical Journal 55.4 (2005): 845-861. <http://eudml.org/doc/30993>.

@article{Lee2005,
abstract = {In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation \[ (r(t)\Phi (u^\{\prime \}(t)))^\{\prime \}+c(t)\Phi (u(t))=0, \] where (i) $r,c\in C([t_\{0\}, \infty )$, $\mathbb \{R\}:=(-\infty , \infty ))$ and $r(t)>0$ on $[t_\{0\},\infty )$ for some $t_\{0\}\ge 0$; (ii) $\Phi (u)=|u|^\{p-2\}u$ for some fixed number $p> 1$. We also generalize some results of Hille-Wintner, Leighton and Willet.},
author = {Lee, Chung-Fen, Yeh, Cheh Chih, Gau, Chuen-Yu},
journal = {Czechoslovak Mathematical Journal},
keywords = {oscillatory; nonoscillatory; Riccati differential equation; Sturm Comparison Theorem; oscillatory; nonoscillatory; Riccati differential equation; Sturm Comparison Theorem},
language = {eng},
number = {4},
pages = {845-861},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some oscillation theorems for second order differential equations},
url = {http://eudml.org/doc/30993},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Lee, Chung-Fen
AU - Yeh, Cheh Chih
AU - Gau, Chuen-Yu
TI - Some oscillation theorems for second order differential equations
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 845
EP - 861
AB - In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation \[ (r(t)\Phi (u^{\prime }(t)))^{\prime }+c(t)\Phi (u(t))=0, \] where (i) $r,c\in C([t_{0}, \infty )$, $\mathbb {R}:=(-\infty , \infty ))$ and $r(t)>0$ on $[t_{0},\infty )$ for some $t_{0}\ge 0$; (ii) $\Phi (u)=|u|^{p-2}u$ for some fixed number $p> 1$. We also generalize some results of Hille-Wintner, Leighton and Willet.
LA - eng
KW - oscillatory; nonoscillatory; Riccati differential equation; Sturm Comparison Theorem; oscillatory; nonoscillatory; Riccati differential equation; Sturm Comparison Theorem
UR - http://eudml.org/doc/30993
ER -

References

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