Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-16T19:19:41.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear differential equations in reflexive Banach spaces

Published online by Cambridge University Press:  17 April 2009

W.E. Fitzgibbon
W.E. Fitzgibbon
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas, USA.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be a reflexive Banach space and be a family of weakly continuous operators which map X to X. Conditions are provided which guarantee the existence and the uniqueness to the Cauchy initial value problem

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 1 , February 1974 , pp. 31 - 37
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Browder, Fellx E., “Non-linear equations of evolution”, Ann. of Math. (2) 80 (1964), 485–523.CrossRefGoogle Scholar
[2]Chow, Shul-nee and Schuur., J.D., “An existence theorem for ordinary differential equations in Banach spaces”, Bull. Amer. Math. Soc. 77 (1971), 1018–1020.CrossRefGoogle Scholar
[3]Diaz, J.B. and Weinacht, R.J., “On nonlinear differential equations in Hilbert spaces”, Applicable Anal. 1 (1971), 31–41.CrossRefGoogle Scholar
[4]Fitzgibbon., W.E., “Weakly continuous accretive operators”, Bull. Amer. Math. Soc. 79 (1973), 473–474.CrossRefGoogle Scholar
[5]Fitzgibbon., W.E., “Weakly continuous accretive operators in reflexive Banach spaces”, Proc. Amer. Math. Soc. (to appear).Google Scholar
[6]Goldstein, Jerome A., “Uniqueness for nonlinear Cauchy problems in Banach spaces”, Applicable Anal. (to appear).Google Scholar
[7]Kato, Toslo, “Nonlinear semigroups and evolution equations”, J. Math. Soc. Japan 19 (1967), 508–520.CrossRefGoogle Scholar
[8]Kato, Toslo, “Accretive operators and nonlinear evolution equations in Banach spaces”, Nonlinear functional analysis, 138–161 (Proc. Sympos. Pure Math. 18, Part 1, Chicago, Illinois, 1968. Amer. Math. Soc., Providence, Rhode Island, 1970).CrossRefGoogle Scholar
[9]Martin, R.H. Jr, “A global existence theorem for autonomous differential equations in a Banach space”, Proc. Amer. Math. Soc. 26 (1970), 307–314.CrossRefGoogle Scholar
[10]Martin, Robert H. Jr, “The logarithmic derivative and equations of evolution in a Banach space”, J. Math. Soc. Japan 22 (1970), 411–429.CrossRefGoogle Scholar
[11]Medeiros., L.A., “On nonlinear differential equations in Hilbert spaces”, Amer. Math. Monthly 76 (1969), 1024–1027.CrossRefGoogle Scholar
[12]Webb., G.A., “Continuous nonlinear perturbations of linear accretive operators in Banach spaces”, J. Functional Analysis 10 (1972), 191–203.CrossRefGoogle Scholar