×

On a singular problem of Cauchy-Nicoletti. (English) Zbl 0307.34003


MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] G. A. Bessmertnych,Some notes on the problem of existence of a solution for singular systems of ordinary differential equations (Russian), Pribl. Met. Reš. Diff. Uravn., Vip. 2, Kiev, « Naukova Dumka » (1960), pp. 23-30.
[2] J. Guseinov - A. I. Perov,The singular problem of Cauchy for nonlinear equations in a Hilbert space (Russian), Uč. zap. Azerb. Un-ta, ser. fiz.-matem.n., no. 3 (1964), pp. 41-50.
[3] Kiguradze, I. T., On the Cauchy problem for singular systems of ordinary differential equations, Diff. Uravnenia, 1, 10, 1271-1289 (1965)
[4] Kiguradze, I. T., The comparison lemma and the question of uniquenss for solutions of the Cauchy problem for differential equations, Soobšč. Akad. Nauk Gruzin. SSR, 39, 3, 513-518 (1965) · Zbl 0143.10803
[5] Kiguradze, I. T., On the singular problem of Nicoletti, Soviet Math. Dokl., 10, 3, 769-772 (1969) · Zbl 0193.04901
[6] Lasota, A., Sur l’existence et l’unicité solutions du problème aux limites de Nicoletti pour un système d’équations différentielles ordinaires, Zeszyty Nauk, UJ, Prace Mat., 11, 41-48 (1966) · Zbl 0286.34025
[7] Lasota, A.; Olech, C., An optimal solution of Nicoletti’s boundary value problem, Ann. Polon. Math., 18, 2, 131-139 (1966) · Zbl 0144.10301
[8] Levin, V. I., On inequalities, Matem. Sbornik, 9, 46, 309-324 (1938) · Zbl 0021.01801
[9] Nicoletti, O., Sulle condizioni iniziali che determinano gli integrali della equazioni differenziali ordinarie, Atti d. R. Acc. Sc. Torino, 33, 746-759 (1897) · JFM 29.0261.02
[10] Perov, A. I., On the singular problem of Cauchy, Trudi Semin. po funk. annal. Voronešskii, Universitet, 7, 104-107 (1963)
[11] Perov, A. I.; Kibenko, A. V., On one general way of studying boundary value problems, Izv. AN SSSR, Ser. matem., 30, 2, 249-264 (1966)
[12] Skripnik, V. P., On one boundary value problem and questions of oscillations of solutions, Matem. Sbornik, 55, 97, 449-472 (1961) · Zbl 0119.07602
[13] Čečik, V. A., The investigation of systems of ordinary differential equations with the singularity, Trudy Mosk. matem. obšč., 8, 155-197 (1959)
[14] Cinquini, S., A proposito dell’esistenza della soluzione di problema di Nicoletti per sistemi di equazioni differenziali ordinarie, Rend. Ist. Lombardo Accad. Sci. e Lettere, 101, 1, 3-7 (1967) · Zbl 0204.10102
[15] Schauder, J., Der Fixpunktsatz in Funktionalräumen, Studia Math., 2, 171-180 (1930) · JFM 56.0355.01
[16] Švec, M., K problému jednoznačnosti integràlov systému lineárnych differenciálnich rovnic, Matem.-Fyz. Sb. SAV, 2, 1-2, 3-22 (1952)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.