| Title:
|
Conjugacy and disconjugacy criteria for second order linear ordinary differential equations (English) |
| Author:
|
Chantladze, T. |
| Author:
|
Lomtatidze, A. |
| Author:
|
Ugulava, D. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
313-323 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Conjugacy and disconjugacy criteria are established for the equation \[ u^{\prime \prime }+p(t)u=0\,, \] where $p:]-\infty ,+\infty [\rightarrow ]-\infty ,+\infty [$ is a locally summable function. (English) |
| Keyword:
|
second order equation |
| Keyword:
|
conjugacy criteria |
| Keyword:
|
disconjugacy criteria |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1054.34053 |
| idMR:
|
MR1811176 |
| . |
| Date available:
|
2008-06-06T22:26:28Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107746 |
| . |
| Reference:
|
[1] Ahlbrandt C. D., Hinton D. B., Lewis R. T.: The effect of variable change on oscillation and disconjugacy criteria with applications to spectral and asymptotic theory.J. Math. Anal. Appl., vol. 81 (1981), pp. 234–277. MR 0618771 |
| Reference:
|
[2] Chanturia T. A.: On conjugacy of high order ordinary differential equations.Georgian Math. J., vol. 1 (1994), No. 1, 1–8. MR 1251490 |
| Reference:
|
[3] Chantladze T., Kandelaki N., Lomtatidze A.: On zeros of solutions of the second order singular half–linear equation.Mem. Differential Equations Math. Phys., vol. 17 (1999), 127–154. MR 1710580 |
| Reference:
|
[4] Chantladze T., Kandelaki N., Lomtatidze A.: Oscillation and nonoscillation criteria for the second order linear equation.Georgian Math. J., vol. 6 (1999), No. 5, 401–414. MR 1692963 |
| Reference:
|
[5] Došlý O.: The multiplicity criteria for zero points of second order differential equations.Math. Slovaca, vol. 42 (1992), No. 2, 181–193. MR 1170102 |
| Reference:
|
[6] Došlý O.: Conjugacy criteria for second order differential equations.Rocky Mountain J. of Math., vol. 23 (1993), No. 3, 849–861. MR 1245450 |
| Reference:
|
[7] Hartman P.: Ordinary differential equations.John Wiley & Sons, Inc., New–York–London–Sydney, 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[8] Hawking S. W., Penrose R.: The singularities of gravitational collapse and cosmology.Proc. Roy. Soc. London, Ser. A, vol. 314 (1970), 529–548. Zbl 0954.83012, MR 0264959 |
| Reference:
|
[9] Mingarelli A. B.: On the existence of conjugate points for the second order ordinary differential equation.SIAM J. Math. Anal., vol. 17 (1986), No. 1, 1–6. MR 0819206 |
| Reference:
|
[10] Müller–Pfeiffer E.: Existence of conjugate points for second and fourth order differential equations.Proc. Roy. Soc. Edinburgh, Sect. A, vol. 89 (1981), 281–291. MR 0635764 |
| Reference:
|
[11] Müller–Pfeiffer E.: Nodal domains of one–or–two–dimensional elliptic differential equations.Z. Anal. Anwendungen, vol. 7 (1988), 135–139. MR 0951346 |
| Reference:
|
[12] Peña S.: Conjugacy criteria for half–linear differential equations.Arch. Math., vol. 35 (1999), No. 1, 1–11. MR 1684518 |
| Reference:
|
[13] Tipler F. J.: General relativity and ordinary differential equations.J. Differential Equations, vol. 30 (1978), 165–174. MR 0513268 |
| Reference:
|
[14] Willet D.: On the oscillatory behaviour of the solutions of second order linear differential equations.Ann. Polon. Math., vol. 21 (1969), 175–194. |
| . |
