| Title:
|
Singular solutions for the differential equation with $p$-Laplacian (English) |
| Author:
|
Bartušek, Miroslav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
123-128 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper a sufficient condition for all solutions of the differential equation with $p$-Laplacian to be proper. Examples of super-half-linear and sub-half-linear equations $(|y^{\prime }|^{p-1} y^{\prime })^{\prime } + r(t) |y|^\lambda \operatorname{sgn}y = 0$, $r>0$ are given for which singular solutions exist (for any $p>0$, $\lambda > 0$, $p\ne \lambda $). (English) |
| Keyword:
|
singular solutions |
| Keyword:
|
noncontinuable solutions |
| Keyword:
|
second order equations |
| MSC:
|
34C10 |
| MSC:
|
34C15 |
| MSC:
|
34D05 |
| idZBL:
|
Zbl 1116.34325 |
| idMR:
|
MR2142148 |
| . |
| Date available:
|
2008-06-06T22:45:23Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107940 |
| . |
| Reference:
|
[1] Bartušek M.: Asymptotic properties of oscillatory solutions of differential equations of $n$-th order.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 1992. MR 1271586 |
| Reference:
|
[2] Bartušek M., Cecchi M., Došlá Z., Marini M.: Global monotonicity and oscillation for second order differential equation.Czechoslovak Math. J., to appear. Zbl 1081.34029, MR 2121668 |
| Reference:
|
[3] Coffman C. V., Ullrich D. F.: On the continuation of solutions of a certain non-linear differential equation.Monatsh. Math. B 71 (1967), 385–392. Zbl 0153.40204, MR 0227494 |
| Reference:
|
[4] Coffman C. V., Wong J. S. W.: Oscillation and nonoscillation theorems for second order differential equations.Funkcial. Ekvac. 15 (1972), 119–130. MR 0333337 |
| Reference:
|
[5] Cecchi M., Došlá Z., Marini M.: On nonoscillatory solutions of differential equations with $p$-Laplacian.Adv. Math. Sci. Appl. 11 (2001), 419–436. Zbl 0996.34039, MR 1842385 |
| Reference:
|
[6] Došlý O.: Qualitative theory of half-linear second order differential equations.Math. Bohem. 127 (2002), 181–195. MR 1981523 |
| Reference:
|
[7] Heidel J. W.: Uniqueness, continuation and nonoscillation for a second order differential equation.Pacific J. Math. 32 (1970), 715–721. MR 0259244 |
| Reference:
|
[8] Mirzov D.: Asymptotic properties of solutions of systems of nonlinear nonautonomous ordinary differential equations.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 14 2004. Zbl 1154.34300, MR 2144761 |
| Reference:
|
[9] Kiguradze I., Chanturia T.: Asymptotic properties of solutions of nonautonomous ordinary differential equations.Kluwer, Dordrecht 1993. Zbl 0782.34002 |
| . |
