| Title:
|
Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian (English) |
| Author:
|
Pekárková, Eva |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
135-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study asymptotic properties of solutions for a system of second differential equations with $p$-Laplacian. The main purpose is to investigate lower estimates of singular solutions of second order differential equations with $p$-Laplacian $(A(t)\Phi _{p}(y^{\prime }))^{\prime }+B(t)g(y^{\prime })+R(t)f(y)=e(t)$. Furthermore, we obtain results for a scalar equation. (English) |
| Keyword:
|
second order differential equation |
| Keyword:
|
$p$-Laplacian |
| Keyword:
|
asymptotic properties |
| Keyword:
|
lower estimate |
| Keyword:
|
singular solution |
| MSC:
|
34A12 |
| MSC:
|
34C11 |
| idZBL:
|
Zbl 1240.34187 |
| idMR:
|
MR2684255 |
| . |
| Date available:
|
2010-06-22T22:11:55Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140309 |
| . |
| Reference:
|
[1] Astašova, I. V.: On asymptotic behaviour of solutions of nonlinear differential equations.Dokl. Semin. Inst. Prikl. Mat. im. I. N. Vekua 1 (3) (1985), 9–11. |
| Reference:
|
[2] Bartušek, M.: On noncontinuable solutions of $n$-th order differential equations.DCDIS A, Supplement, to appear. MR 2518879 |
| Reference:
|
[3] Bartušek, M.: On existence of singular solution of $n$-th order differential equations.Arch. Math. (Brno) 36 (2000), 395–404. MR 1822807 |
| Reference:
|
[4] Bartušek, M.: On existence unbounded noncontinuable solutions.Ann. Mat. Pura Appl. (4) 185 (2006), 93–107. MR 2187756 |
| Reference:
|
[5] Bartušek, M., Graef, J. R.: Strong nonlinear limit-point/limit-circle problem for second order nonlinear equations.Nonlinear Stud. 9 (1) (2006), 361–369. |
| Reference:
|
[6] Bartušek, M., Graef, J. R.: The strong nonlinear limit-point/limit-circle properties for a class of even order equations.Comm. Appl. Nonlinear Anal. 15 (3) (2008), 29–45. Zbl 1165.34325, MR 2441804 |
| Reference:
|
[7] Bartušek, M., Medveď, M.: Existence of global solutions for systems of second-order functional-differential equations with $p$-Laplacian.EJDE 40 (2008), 1–8. Zbl 1171.34335, MR 2392944 |
| Reference:
|
[8] Bartušek, M., Osička, J.: On existence of singular solutions.Georgian Math. J. 8 (2001), 669–681. MR 1884492 |
| Reference:
|
[9] Bartušek, M., Pekárková, E.: On existence of proper solutions of quasilinear second order differential equations.EJQTD 1 (2007), 1–14. Zbl 1115.34032 |
| Reference:
|
[10] Bartušková, I.: Problem of Computations of Sewerage Systems.Ph.D. thesis, FAST Technical University Brno, 1997, in Czech. |
| Reference:
|
[11] Chanturia, T.: On existence of singular and unbounded oscillatory solutions of differential equations of Emden-Fowler type.Differ. Uravn. 28 (1992), 1009–1022. MR 1198158 |
| Reference:
|
[12] Jaroš, J., Kusano, T.: On black hole solutions of second order differential equation with singularity in the diffential operator.Funkcial. Ekvac. 43 (2000), 491–509. MR 1815473 |
| Reference:
|
[13] Kiguradze, I. T., Chanturia, T.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Dordrecht, Kluwer, 1993. Zbl 0782.34002 |
| Reference:
|
[14] Medveď, M., Pekárková, E.: Existence of global solutions of systems of second order differential equations with $p$-Laplacian.EJDE 136 (2007), 1–9. |
| Reference:
|
[15] Mirzov, J. D.: Asymptotic Properties of Solutions of System of Nonlinear Nonautonomous Differential Equations.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 14 (2004). MR 2144761 |
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