×

zbMATH — the first resource for mathematics

Local existence of solutions for ordinary differential equations involving dissipative and compact functions. (English) Zbl 0684.34061
Summary: We prove an existence theorem for the Cauchy problem for ordinary differential equations in Banach spaces. This theorem includes known results.

MSC:
34G10 Linear differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arrate, M; Garcia, A.G, On existence uniqueness and approximation of solutions of ordinary differential equations in Banach spaces, J. London math. soc. (2), 27, 121-129, (1983) · Zbl 0535.34045
[2] Deimling, K, Ordinary differential equations in Banach spaces, () · Zbl 0555.60036
[3] Emmanuele, G, Existence of solutions of ordinary differential equations involving dissipative and compact operators in Gelfand-Phillips spaces, J. math. anal. appl., 120, 557-560, (1986) · Zbl 0605.34002
[4] Fleet, T.M, Some applications of Zygmund’s lemma to nonlinear differential equations in Banach and Hilbert spaces, Studia math., 44, 335-344, (1972) · Zbl 0231.34053
[5] Lakshmikantham, V; Leela, S, Nonlinear differential equations in abstract spaces, (1981), Pergamon Oxford · Zbl 0456.34002
[6] Martin, R.H, Differential equations on closed subsets of a Banach space, Trans. amer. math. soc., 179, 399-414, (1973) · Zbl 0293.34092
[7] Martin, R.H, Remarks on ordinary differential equations involving dissipative and compact operators, J. London math. soc. (2), 10, 61-65, (1975) · Zbl 0305.34092
[8] Samimi, M; Lakshmikantham, V, General uniqueness criteria for ordinary differential equations, Appl. math. comput., 12, No. 1, 77-88, (1989) · Zbl 0507.34004
[9] Schechter, E, Evolution generated by continuous dissipative plus compact operators, Bull. London math. soc., 13, 303-308, (1981) · Zbl 0443.34061
[10] Volkmann, P, Ein existenzsatz für gewöhnliche differentialgleichungen in banachräumen, (), 297-300 · Zbl 0506.34051
[11] Volkmann, P, On the convergence of approximate solutions for an initial value problem in Banach spaces, Nonlinear anal., No. 2, 217-222, (1989) · Zbl 0511.34048
[12] Wazewski, T, Sur l’existence et l’unicité des intégrales des équations différentielles ordinaires au cas the l’espace de Banach, Bull. acad. polon. sci. math. astr. phys., 8, 301-305, (1960) · Zbl 0093.08405
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.