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Ein Existenzsatz für gewöhnliche Differentialgleichungen in Banachräumen


Author: Peter Volkmann
Journal: Proc. Amer. Math. Soc. 80 (1980), 297-300
MSC: Primary 34G20
DOI: https://doi.org/10.1090/S0002-9939-1980-0577763-5
MathSciNet review: 577763
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Abstract: A positive answer will be given to the question in the books of Martin [4] and Deimling [2], whether initial value problems for ordinary differential equations in Banach spaces are locally solvable, provided the right-hand side of the equation is the sum of two operators of dissipative and compact type, respectively (see Theorem 2 below).


References [Enhancements On Off] (What's this?)

  • [1] K. Deimling, On existence and uniqueness for differential equations, Ann. Mat. Pura Appl. (4) 106 (1975), 1-10. MR 0481329 (58:1449)
  • [2] -, Ordinary differential equations in Banach spaces, Lecture Notes in Math., Vol. 596, Springer-Verlag, Berlin and New York, 1977. MR 0463601 (57:3546)
  • [3] A. Lasota and J. A. Yorke, The generic property of existence of solutions of differential equations in Banach space, J. Differential Equations 13 (1973), 1-12. MR 0335994 (49:770)
  • [4] R. H. Martin, Jr., Nonlinear operators and differential equations in Banach spaces, Wiley, New York, 1976. MR 0492671 (58:11753)
  • [5] S. Szufla, Some remarks on ordinary differential equations in Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 795-800. MR 0239238 (39:595)

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DOI: https://doi.org/10.1090/S0002-9939-1980-0577763-5
Article copyright: © Copyright 1980 American Mathematical Society

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