Ein Existenzsatz für gewöhnliche Differentialgleichungen in Banachräumen

Volkmann, Peter

doi:10.1090/S0002-9939-1980-0577763-5

Ein Existenzsatz für gewöhnliche Differentialgleichungen in Banachräumen
HTML articles powered by AMS MathViewer

by Peter Volkmann

Proc. Amer. Math. Soc. 80 (1980), 297-300

DOI: https://doi.org/10.1090/S0002-9939-1980-0577763-5

PDF | Request permission

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

Klaus Deimling, On existence and uniqueness for differential equations, Ann. Mat. Pura Appl. (4) 106 (1975), 1–10. MR 481329, DOI 10.1007/BF02415020
Klaus Deimling, Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics, Vol. 596, Springer-Verlag, Berlin-New York, 1977. MR 0463601, DOI 10.1007/BFb0091636
A. Lasota and James A. Yorke, The generic property of existence of solutions of differential equations in Banach space, J. Differential Equations 13 (1973), 1–12. MR 335994, DOI 10.1016/0022-0396(73)90027-2
Robert H. Martin Jr., Nonlinear operators and differential equations in Banach spaces, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1976. MR 0492671
S. Szufla, Some remarks on ordinary differential equations in Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 795–800 (English, with Russian summary). MR 239238