Title:
|
Integral averages and oscillation of second order sublinear differential equations (English) |
Author:
|
Manojlović, Jelena V. |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
55 |
Issue:
|
1 |
Year:
|
2005 |
Pages:
|
41-60 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
New oscillation criteria are given for the second order sublinear differential equation \[ [a(t)\psi (x(t))x^{\prime }(t)]^{\prime }+q(t)f(x(t))=0, \quad t\ge t_0>0, \] where $a\in C^1([t_0,\infty ))$ is a nonnegative function, $\psi , f\in C({\mathbb R})$ with $\psi (x)\ne 0$, $xf(x)/\psi (x)>0$ for $x\ne 0$, $\psi $, $f$ have continuous derivative on ${\mathbb R}\setminus \lbrace 0\rbrace $ with $[f(x)/\psi (x)]^{\prime }\ge 0$ for $x\ne 0$ and $q\in C([t_0,\infty ))$ has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients $q$ and $a$ and extend known oscillation criteria for the equation $x^{\prime \prime }(t)+q(t)x(t)=0$. (English) |
Keyword:
|
oscillation |
Keyword:
|
sublinear differential equation |
Keyword:
|
integral averages |
MSC:
|
34C10 |
MSC:
|
34C15 |
MSC:
|
34C29 |
idZBL:
|
Zbl 1081.34032 |
idMR:
|
MR2121655 |
. |
Date available:
|
2009-09-24T11:20:46Z |
Last updated:
|
2020-07-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127958 |
. |
Reference:
|
[1] B. Ayanlar and A. Tiryaki: Oscillation theorems for nonlinear second-order differential equations.Comput. Math. Appl. 44 (2002), 529–538. MR 1912848, 10.1016/S0898-1221(02)00167-0 |
Reference:
|
[2] Y. Chen: On the oscillation of nonlinear second order equations.J. South China Normal Univ. Natur. Sci. Ed. 2 (1986), 99–103. MR 1005446 |
Reference:
|
[3] S. R. Grace and B. S. Lalli: On the second order nonlinear oscillations.Bull. Inst. Math. Acad. Sinica 15 (1987), 297–309. MR 0942790 |
Reference:
|
[4] S. R. Grace: Oscillation theorems for second order nonlinear differential equations with damping.Math. Nachr. 141 (1989), 117–127. Zbl 0673.34041, MR 1014421, 10.1002/mana.19891410114 |
Reference:
|
[5] S. R. Grace and B. S. Lalli: Integral averaging techniques for the oscillation of second order nonlinear differential equations.J. Math. Anal. and Appl. 149 (1990), 277–311. MR 1054809, 10.1016/0022-247X(90)90301-U |
Reference:
|
[6] S R. Grace: Oscillation theorems for nonlinear differential equations of second order.J. Math. Anal. and Appl. 171 (1992), 220–241. Zbl 0767.34017, MR 1192503, 10.1016/0022-247X(92)90386-R |
Reference:
|
[7] M. Kirane and Y. V. Rogovchenko: Oscillation results for a second order damped differential equation with nonmonotonous nonlinearity.J. Math. Anal. Appl. 250 (2000), 118–138. MR 1893881, 10.1006/jmaa.2000.6975 |
Reference:
|
[8] T. Kura: Oscillation theorems for second order nonlinear differential equations.Proc. Amer. Math. Soc. 84 (1982), 535–538. MR 0643744, 10.1090/S0002-9939-1982-0643744-8 |
Reference:
|
[9] M. K. Kwong and J. S. W. Wong: On an oscillation theorem of Belohorec.SIAM J. Math. Anal. 14 (1983), 474–476. MR 0697523, 10.1137/0514040 |
Reference:
|
[10] H. J. Li and C. C. Yeh: Oscillation of second order sublinear differential equations.Dynamic Systems Appl. 6 (1997), 529–534. MR 1487476 |
Reference:
|
[11] J. V. Manojlović: Oscillation criteria for second order sublinear differential equation.Math. Comp. Modelling 30 (1999), 109–119. MR 1753568, 10.1016/S0895-7177(99)00151-X |
Reference:
|
[12] J. V. Manojlović: Oscillation criteria for second order sublinear differential equation.Computers and Mathematics with Applications 39 (2000), 161–172. 10.1016/S0898-1221(00)00094-8 |
Reference:
|
[13] J. V. Manojlović: Integral averages and oscillation of second order nonlinear differential equations.Computers and Mathematics with Applications 41 (2001), 1521–1534. MR 1831815, 10.1016/S0898-1221(01)00117-1 |
Reference:
|
[14] Ch. G. Philos: Oscillation of sublinear differential equations of second order.Nonlinear Anal. 7 (1983), 1071–1080. Zbl 0525.34028, MR 0719359, 10.1016/0362-546X(83)90016-0 |
Reference:
|
[15] Ch. G. Philos: On second order sublinear oscillation.Aequationes Math. 27 (1984), 242–254. Zbl 0545.34026, MR 0762684, 10.1007/BF02192675 |
Reference:
|
[16] Ch. G. Philos: Integral averaging techniques for the oscillation of second order sublinear ordinary differential equations.J. Austral. Math. Soc. (Series A) 40 (1986), 111–130. Zbl 0583.34028, MR 0809730, 10.1017/S1446788700026549 |
Reference:
|
[17] Ch. G. Philos: Oscillation theorems for linear differential equations of second order.Arch. Math. (Basel) 53 (1989), 482–492. Zbl 0661.34030, MR 1019162, 10.1007/BF01324723 |
Reference:
|
[18] Ch. G. Philos: Integral averages and oscillation of second order sublinear differential equations.Diff. Integ. Equat. 4 (1991), 205–213. Zbl 0721.34026, MR 1079621 |
Reference:
|
[19] J. Yan: A note on second order sublinear oscillation theorems.J. Math. Anal. and Appl. 104 (1984), 103–106. Zbl 0609.34045, MR 0765043, 10.1016/0022-247X(84)90034-9 |
Reference:
|
[20] J. S. W. Wong: An oscillation criterion for second order sublinear differential equations.Conf. Proc. Canad. Math. Soc. 8 (1987), 299–302. Zbl 0624.34027, MR 0909919 |
Reference:
|
[21] J. S. W. Wong and C. C. Yeh: An oscillation criterion for second order sublinear differential equations.J. Math. Anal. Appl. 171 (1992), 346–351. MR 1194084, 10.1016/0022-247X(92)90348-H |
Reference:
|
[22] J. S. W. Wong: Oscillation criteria for second order nonlinear differential equations involving general means.J. Math. Anal. Appl. 247 (2000), 489–505. Zbl 0964.34028, MR 1769091, 10.1006/jmaa.2000.6855 |
. |