Existence results for infinite dimensional differential equations without compactness

Giovanni Colombo; Barnabas M. Garay

Rendiconti del Seminario Matematico della Università di Padova (1994)

  • Volume: 92, page 127-133
  • ISSN: 0041-8994

How to cite

top

Colombo, Giovanni, and Garay, Barnabas M.. "Existence results for infinite dimensional differential equations without compactness." Rendiconti del Seminario Matematico della Università di Padova 92 (1994): 127-133. <http://eudml.org/doc/108330>.

@article{Colombo1994,
author = {Colombo, Giovanni, Garay, Barnabas M.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Banach space; Cauchy problem; existence},
language = {eng},
pages = {127-133},
publisher = {Seminario Matematico of the University of Padua},
title = {Existence results for infinite dimensional differential equations without compactness},
url = {http://eudml.org/doc/108330},
volume = {92},
year = {1994},
}

TY - JOUR
AU - Colombo, Giovanni
AU - Garay, Barnabas M.
TI - Existence results for infinite dimensional differential equations without compactness
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1994
PB - Seminario Matematico of the University of Padua
VL - 92
SP - 127
EP - 133
LA - eng
KW - Banach space; Cauchy problem; existence
UR - http://eudml.org/doc/108330
ER -

References

top
  1. [1] A. Cellina, On the nonexistence of solutions of differential equations in nonreflexive spaces, Bull. Amer. Math. Soc., 78 (1972), pp. 1069-1072. Zbl0277.34066MR312017
  2. [2] A. Cellina, On the local existence of solutions of ordinary differential equations, Bull. Pol. Acad. Sci., 20 (1972), pp. 293-296. Zbl0255.34053MR315237
  3. [3] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lecture Notes in Math., No. 596, Springer, Berlin (1977). Zbl0361.34050MR463601
  4. [4] J. Dieudonné, Deux exemples singuliers d'équations différentielles, Acta Sci. Math.(Szeged), 12 (1950), pp. 38-40. Zbl0037.06002MR35397
  5. [5] B.M. Garay, Deleting homeomorphisms and the failure of Peano's existence theorem in infinite-dimensional Banach spaces, Funkcial. Ekvac., 34 (1991), pp. 85-93. Zbl0734.34055MR1116881
  6. [6] A.N. Godunov, The Peano theorem in Banach spaces, Funktsional. Anal. i Prilozhen., 9 (1975), pp. 59-60 (Russian). Zbl0314.34059MR364797
  7. [7] K. Goebel - J. Wosko, Making a hole in the space, Proc. Amer. Math. Soc., 114 (1992), pp. 475-476. Zbl0747.46011MR1065949
  8. [8] V. Lakshmikantham - S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon, Oxford (1981). Zbl0456.34002MR616449
  9. [9] A. Lasota - J.A. Yorke, The generic property of existence of solutions of differential equations in Banach spaces, J. Differ. Equat., 13 (1973), pp. 1-12. Zbl0259.34070MR335994
  10. [10] R.H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York (1976). Zbl0333.47023MR492671
  11. [11] N.H. Paves, Nonlinear Evolution Operators and Semigroups: Applications to Partial Differential Equations, Lecture Notes in Math., No. 1260, Springer, Berlin (1987). Zbl0626.35003MR900380
  12. [12] J. Saint-Raymond, Une équation différentielle sans solution, in: Initiation Seminar on Analysis: 1980/81, Comm. No. C2, 7 pp., Publ. Math. Univ. P. et M. Curie, 46, Univ. Paris VI, Paris (1981). Zbl0534.34005MR670806
  13. [13] E. Schechter, A survey of local existence theories for abstract nonlinear initial value problems, in: Nonlinear Semigroups, PDE's and Attractors, edited by T. L. GILL and W. W. ZACHARY, Lecture Notes in Mathematics, No. 1394, Springer, Berlin (1989), pp. 136-184. Zbl0678.34005MR1021021
  14. [14] S. Schmidt, Zwei Existenzsätze für gewöhnliche Differentialgleichungen in Banachräumen, Comment. Math. Prace Mat., 28 (1989), pp. 345-353. Zbl0681.34054MR1024948
  15. [15] S. Schmidt, Existenzsätze für gewöhnliche Differentialgleichungen in Banachräumen, Funkcial. Ekvac., 35 (1992), pp. 199-222. Zbl0785.34045MR1189893

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.