| Title:
|
Conjugacy criteria for half-linear differential equations (English) |
| Author:
|
Peňa, Simón |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
1-11 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient conditions on the function $c(t)$ ensuring that the half-linear second order differential equation \[ (|u^\prime |^{p-2} u^\prime )^\prime + c(t)|u(t)|^{p-2} u(t)=0\,, \quad \quad p>1 \] possesses a nontrivial solution having at least two zeros in a given interval are obtained. These conditions extend some recently proved conjugacy criteria for linear equations which correspond to the case $p=2$. (English) |
| Keyword:
|
half-linear equation |
| Keyword:
|
scalar p-Laplacian |
| Keyword:
|
conjugate points |
| Keyword:
|
conjugacy criteria |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1054.34055 |
| idMR:
|
MR1684518 |
| . |
| Date available:
|
2008-06-06T22:22:24Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107680 |
| . |
| Reference:
|
[1] Došlý, O.: Conjugacy criteria for second order differential equations.Rocky Mountain, J. Math. 23(1993), 849-861. MR 1245450 |
| Reference:
|
[2] Elbert, Á.: A half-linear second order differential equation.Colloquia Math. Soc. Janos Bolyai, 30, Qualitative theory of differential equation, Szeged (1979), 153-180. Zbl 0511.34006, MR 0680591 |
| Reference:
|
[3] Harris, B. J., Kong, Q.: On the oscillation of differential equations with an oscillatory coefficient.Trans. Amer. Math. Soc. 347(1995), 1831-1839. MR 1283552 |
| Reference:
|
[4] Li, H. J., Yeh, C. Ch.: Oscillations of half-linear second order differential equations.Hiroshima Math. J. 25(1995), 585-594. MR 1364076 |
| Reference:
|
[5] Müller-Pfeiffer, E.: Existence of conjugate points for second and fourth order differential equations.Proc. Roy. Soc. Edinburgh Sect. A 89(1981), 281-291. MR 0635764 |
| Reference:
|
[6] Tipler, F. J.: General relativity and conjugate ordinary differential equations.J. Diff. Equations 30(1978), 165-174. Zbl 0362.34023, MR 0513268 |
| . |
