A generalization of Caratheodory’s existence theorems for ordinary differential equations.(English)Zbl 0296.34004

MSC:

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

References:

 [1] Chu, S.C; Diaz, J.B, A fixed point theorem for “in the large” application of the contraction principle, Att. accad. sci. Torino cl. sci. fis. mat. natur., 99, 351-363, (1964-1965) · Zbl 0139.09101 [2] Filippov, A.F; Filippov, A.F, The existence of solutions of generalized differential equations, Math. notes, Mat. zametki, 10, 307-313, (1971), Russian original · Zbl 0221.15011 [3] Goodman, G.S, Subfunctions and initial value problems for differential equations satisfying Carathéodory’s hypothesis, J. differential equations, 7, 232-242, (1970) · Zbl 0276.34003 [4] Kartak, K, A generalization of the Carathéodory theory of differential equations, Czechoslovak math. J., 17, 482-514, (1967) · Zbl 0189.37101 [5] Marchaud, A, Sur LES champs de demi-droites et LES équations différentielles du premier ordre, Bull. soc. math. France, 62, 1-38, (1934) · JFM 60.0373.09 [6] Matrosov, V.M; Matrosov, V.M; Matrosov, V.M; Matrosov, V.M, On differential equations and inequalities with discontinuous right hand sides, Differencial’nye uravenija, Differencial’nye uravenija, Differential equations, Differential equations, 3, 432-437, (1967), Engl. transl. · Zbl 0225.34009 [7] Peetre, J; Persson, J, The Peano existence theorem under weaker assumptions, () [8] Persson, J, An existence theorem for a general Goursat problem, J. differential equations, 5, 461-469, (1969) · Zbl 0174.14601 [9] Persson, J, Theorems for continuous solutions of generalized Goursat problems, Matematiche, 24, 108-136, (1969) · Zbl 0189.40903 [10] Reid, W.T, Ordinary differential equations, (1971), Wiley New York · Zbl 0212.10901 [11] Royden, H.L, Real analysis, (1970), Macmillan London · Zbl 0197.03501 [12] Schauder, J, Der fixpunktsatz in funktionalräumen, Studia math., 2, 171-180, (1930) · JFM 56.0355.01 [13] Dragoni, G.Scorza, Un teorema sulle funzioni continue rispetto ad una variabile e misurabile rispetto ad un’altra, (), 102-106 · Zbl 0032.19702 [14] Viktorovskiǐ, E.E, On a general theorem on existence of solutions of differential equations connected with the use of integral inequalities, Mat. sb., 31, 27-33, (1952) [15] Whyburn, W.M, On the fundamental existence theorems for differential systems, Ann. of math., 30, 31-38, (1929) · JFM 54.0474.02 [16] Zaremba, S.C, Sur LES équations au paratingent, Bull. sci. math., 60, 139-163, (1936) · JFM 62.0507.01
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.