| Title:
|
On the number of zeros of bounded nonoscillatory solutions to higher-order nonlinear ordinary differential equations (English) |
| Author:
|
Naito, Manabu |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
39-53 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The higher-order nonlinear ordinary differential equation \[ x^{(n)} + \lambda p(t)f(x) = 0\,, \quad t \ge a\,, \] is considered and the problem of counting the number of zeros of bounded nonoscillatory solutions $x(t;\lambda )$ satisfying $\lim _{t\rightarrow \infty }x(t;\lambda ) = 1$ is studied. The results can be applied to a singular eigenvalue problem. (English) |
| Keyword:
|
nonoscillatory solutions |
| Keyword:
|
zeros of solutions |
| Keyword:
|
singular eigenvalue problems |
| MSC:
|
34B40 |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1164.34014 |
| idMR:
|
MR2310123 |
| . |
| Date available:
|
2008-06-06T22:50:27Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108048 |
| . |
| Reference:
|
[1] Elias U.: Eigenvalue problems for the equation $Ly + \lambda p(x)y = 0$.J. Differential Equations 29 (1978), 28–57. Zbl 0369.34008, MR 0486759 |
| Reference:
|
[2] Elias U.: Oscillation Theory of Two-Term Differential Equations.Kluwer, 1997. Zbl 0878.34022, MR 1445292 |
| Reference:
|
[3] Elias U.: Singular eigenvalue problems for the equation $y^{(n)} + \lambda p(x)y = 0$.Monatsh. Math. 142 (2004), 205–225. MR 2071246 |
| Reference:
|
[4] Elias U., Pinkus A.: Nonlinear eigenvalue problems for a class of ordinary differential equations.Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), 1333–1359. Zbl 1028.34076, MR 1950810 |
| Reference:
|
[5] Hartman P.: Ordinary Differential Equations.Wiley, 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[6] Kiguradze I. T., Chanturia T. A.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Kluwer, 1993. Zbl 0782.34002 |
| Reference:
|
[7] Naito M.: On the number of zeros of nonoscillatory solutions to higher-order linear ordinary differential equations.Monatsh. Math. 136 (2002), 237–242. Zbl 1009.34034, MR 1919646 |
| Reference:
|
[8] Naito M., Naito Y.: Solutions with prescribed numbers of zeros for nonlinear second order differential equations.Funkcial. Ekvac. 37 (1994), 505–520. Zbl 0820.34019, MR 1311557 |
| Reference:
|
[9] Naito Y., Tanaka S.: On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations.Nonlinear Anal. 56 (2004), 919–935. Zbl 1046.34038, MR 2036055 |
| . |
