| Title:
|
On the Vallée-Poussin problem for singular differential equations with deviating arguments (English) |
| Author:
|
Kiguradze, Ivan |
| Author:
|
Půža, Bedřich |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
127-138 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For the differential equation \[ u^{(n)}(t)= f(t,u(\tau _{1}(t)),\dots ,u^{(n-1)}(\tau _{n}(t))), \] where the vector function $ f:\ ]a,b[\,\times {R}^{kn} \rightarrow {R}^{k}$ has nonintegrable singularities with respect to the first argument, sufficient conditions for existence and uniqueness of the Vallée–Poussin problem are established. (English) |
| Keyword:
|
singular differential equation with deviating arguments |
| Keyword:
|
the Valée-Poussin problem |
| Keyword:
|
existence theorem |
| Keyword:
|
uniqueness theorem |
| MSC:
|
34B10 |
| idZBL:
|
Zbl 0914.34064 |
| idMR:
|
MR1464307 |
| . |
| Date available:
|
2008-06-06T21:32:52Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107603 |
| . |
| Reference:
|
[1] Bessmertnych G. A.: On existence and uniqueness of solutions of multipoint Vallée-Poussin problem for nonlinear differential equaitions.Differentsial’nyje Uravnenija 6, No 2 (1970), 298-310 (in Russian). MR 0267183 |
| Reference:
|
[2] de la Vallée-Poussin Ch. J.: Sur l’equation differentielle lineaire de second ordre. Détermination d’une integrale par deux valeurs assignées. Extension aux équations d’ordre $n$.J. Math. pures et appl. 8, No 2 (1929), 125-144. |
| Reference:
|
[3] Kiguradze I. T.: On a singular multi-point boundary value problem.Ann. Mat. Pura ed Appl. 86(1970), 367-399. Zbl 0251.34012, MR 0271449 |
| Reference:
|
[4] Kiguradze I. T.: Some singular boundary value problems for ordinary differential equations.Tbilisi: Tbilisi University Press (1975) (in Russian). Zbl 0521.34019, MR 0499402 |
| Reference:
|
[5] Kiguradze I. T.: On some singular boundary value problems for ordinary differential equations.Equadiff 5 Proc. 5 Czech. Conf. Diff. Equations and Appl. Leipzig: Teubner Verlagsgesselschaft (1982), 174-178. Zbl 0521.34019 |
| Reference:
|
[6] Kiguradze I. T.: On the solvability of the Valée-Poussin problem.Differentsial’nyje Uravnenija 21, No 3 (1985), 391-398. MR 0785447 |
| Reference:
|
[7] Kiguradze I. T.: On a boundary value problems for higher ordinary differential equations with singularities.Uspekhi Mat. Nauk 41, No. 4 (1986), 166-167 (in Russian). |
| Reference:
|
[8] Kiguradze I., Tskhovrebadze G.: On the two-point boundary value problems for systems of higher order ordinary differential equations with singularities.Georgian Math. J. 1, No 1(1994), 31-45. |
| Reference:
|
[9] Lasota A., Opial Z.: L’existence et l’unicité des solutions du probléme d’interpolation differentielle ordinaire d’ordre $n$.Ann. Polon. Math. 15, No 3(1964), 253-271. MR 0173804 |
| Reference:
|
[10] Levin A. J.: Nonoscillatory solutions of equation $x^{(n)}+ p_1(t) x^{(n-1)}+ \dots + p_n(t)x=0 $.Uspekhi Mat. Nauk 24, No 2(1969), 43-96 (in Russian). |
| Reference:
|
[11] Levin A. J.: On a multi-point boundary value problem.Nauchnie Dokl. Vis. Shkoli 5 (1958), 34-37 (in Russian). |
| Reference:
|
[12] Opial Z.: Linear problems for systems of nonlinear differential equations.J. Diff. Equat. 3, No 4(1967), 580-594. Zbl 0161.06102, MR 0216068 |
| Reference:
|
[13] Sansone G.: Equazioni Differenzialli nel campo reale.Bologna: Zanichelli (1948). MR 0026731 |
| Reference:
|
[14] Tskhovrebadze G. D.: On a multipoint boundary value problem for nonlinear ordinary differential equations with singularities.Arch. Math. 30, No 3(1994), 171-206. MR 1308353 |
| . |
