| Title:
|
Zeros of derivatives of solutions to singular $(p,n-p)$ conjugate BVPs (English) |
| Author:
|
Rachůnková, Irena |
| Author:
|
Staněk, Svatoslav |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
137-141 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Positive solutions of the singular $(p,n-p)$ conjugate BVP are studied. The set of all zeros of their derivatives up to order $n-1$ is described. By means of this, estimates from below of the solutions and the absolute values of their derivatives up to order $n-1$ on the considered interval are reached. Such estimates are necessary for the application of the general existence principle to the BVP under consideration. (English) |
| Keyword:
|
singular conjugate BVP |
| Keyword:
|
positive solutions |
| Keyword:
|
zeros of derivatives |
| Keyword:
|
estimates from below |
| MSC:
|
34B15 |
| MSC:
|
34B16 |
| MSC:
|
34B18 |
| idZBL:
|
Zbl 1068.34018 |
| idMR:
|
MR2124611 |
| . |
| Date available:
|
2009-08-21T12:55:01Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132938 |
| . |
| Reference:
|
[1] Agarwal R. P., O’Regan D.: Positive solutions for (p,n-p) conjugate boundary value problems.J. Differential Equations 150 (1998), 462–473. Zbl 0920.34027, MR 1658664 |
| Reference:
|
[2] Agarwal R. P., O’Regan D.: Multiplicity results for singular conjugate, focal, and $(n,p)$ problems.J. Differential Equations 170 (2001), 142–156. Zbl 0978.34018, MR 1813103 |
| Reference:
|
[3] Agarwal R. P., O’Regan D., Rachůnková I., Staněk S.: Two-point higher order BVPs with singularities in phase variables.Computers & Mathematics with Applications 46 (2003), 1799–1826. Zbl 1057.34005, MR 2018767 |
| Reference:
|
[4] Eloe P. W., Henderson J.: Singular nonlinear $(n-1,1)$ conjugate boundary value problems.Georgian Math. J. 4 (1997), 401–412. Zbl 0882.34029, MR 1469324 |
| Reference:
|
[5] Eloe P. W., Henderson J.: Singular nonlinear $(k,n-k)$ conjugate boundary value problems.J. Differential Equations 133 (1997), 136–151. Zbl 0870.34031, MR 1426760 |
| Reference:
|
[6] Rachůnková I., Staněk S.: General existence principle for singular BVPs and its applications.Georgian Math. J. 11 (2004), 549–565. MR 2081745 |
| . |
