Existence for implicit differential equations in Banach spaces

Viorel Barbu; Angelo Favini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1992)

  • Volume: 3, Issue: 3, page 203-215
  • ISSN: 1120-6330

Abstract

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We prove two existence results on abstract differential equations of the type d ⁢ B ⁢ u / d ⁢ t + A ⁢ u = f and we give some applications of them to partial differential equations.

How to cite

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Barbu, Viorel, and Favini, Angelo. "Existence for implicit differential equations in Banach spaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 3.3 (1992): 203-215. <http://eudml.org/doc/244126>.

@article{Barbu1992,
abstract = {We prove two existence results on abstract differential equations of the type \( d(Bu)/dt + A(u) = f \) and we give some applications of them to partial differential equations.},
author = {Barbu, Viorel, Favini, Angelo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {abstract differential equations; degenerate differential equations; nonlinear monotone operators; Banach space; semilinear; linear operator; Hilbert space},
language = {eng},
month = {9},
number = {3},
pages = {203-215},
publisher = {Accademia Nazionale dei Lincei},
title = {Existence for implicit differential equations in Banach spaces},
url = {http://eudml.org/doc/244126},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Barbu, Viorel
AU - Favini, Angelo
TI - Existence for implicit differential equations in Banach spaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1992/9//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 3
SP - 203
EP - 215
AB - We prove two existence results on abstract differential equations of the type \( d(Bu)/dt + A(u) = f \) and we give some applications of them to partial differential equations.
LA - eng
KW - abstract differential equations; degenerate differential equations; nonlinear monotone operators; Banach space; semilinear; linear operator; Hilbert space
UR - http://eudml.org/doc/244126
ER -

References

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  2. BARBU, V., Nonlinear Semigroups and Differential Equations in Banach Spaces. Nordhoff, Leyden1976. Zbl0328.47035MR390843
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  11. DI BENEDETTO, E. - SHOWALTER, R. E., Implicit degenerate equations and applications. SIAM J. Math. Anal., 12, 1981, 731-751. Zbl0477.47037MR625829DOI10.1137/0512062
  12. FAVINI, A., Abstract potential operators and spectral methods for a class of degenerate evolution problems. J. Diff. Eqs., 39, 1981, 212-225. Zbl0422.34025MR607782DOI10.1016/0022-0396(81)90073-5
  13. FAVINI, A. - YAGI, A., Multivalued linear operators and degenerate evolution equations. Annali di Mat. Pura Appl., to appear. Zbl0786.47037MR1219605DOI10.1007/BF01759029
  14. GRANGE, O. - MIGNOT, F., Sur la résolution d'une équation et d'une inequation parabolique non-linéaire. J. Funct. Anal., 11, 1972, 77-92. Zbl0251.35055MR350207
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