On the structure of solution sets of differential equations in Banach spaces

Daria Bugajewska

Mathematica Slovaca (2000)

  • Volume: 50, Issue: 4, page 463-471
  • ISSN: 0232-0525

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Bugajewska, Daria. "On the structure of solution sets of differential equations in Banach spaces." Mathematica Slovaca 50.4 (2000): 463-471. <http://eudml.org/doc/31529>.

@article{Bugajewska2000,
author = {Bugajewska, Daria},
journal = {Mathematica Slovaca},
keywords = {Aronszajn-type theorem; Cauchy problem; Kuratowski measure of noncompactness; axiomatic measure of noncompactness},
language = {eng},
number = {4},
pages = {463-471},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On the structure of solution sets of differential equations in Banach spaces},
url = {http://eudml.org/doc/31529},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Bugajewska, Daria
TI - On the structure of solution sets of differential equations in Banach spaces
JO - Mathematica Slovaca
PY - 2000
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 50
IS - 4
SP - 463
EP - 471
LA - eng
KW - Aronszajn-type theorem; Cauchy problem; Kuratowski measure of noncompactness; axiomatic measure of noncompactness
UR - http://eudml.org/doc/31529
ER -

References

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  1. AMBROSETTI A., Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Mat. Univ. Padova 39 (1967), 349-360. (1967) Zbl0174.46001MR0222426
  2. BANAS J.-GOEBEL K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math. 60, Marcel Dekker, New York-Basel, 1980. (1980) Zbl0441.47056MR0591679
  3. BUGAJEWSKA D., A note on the global solutions of the Cauchy problem in Banach spaces, Acta Math. Hungar. (To appear). MR1789046
  4. BUGAJEWSKA D., On topological structure of solution sets for delay and functional differential equations, (Submitted). Zbl1003.34063
  5. BUGAJEWSKA D.-BUGAJEWSKI. D., On nonlinear equations in Banach spaces and axiomatic measures of noncompactness, Funct. Differ. Equ. 5 (1998), 57-68. (1998) Zbl1049.45013MR1681184
  6. BUGAJEWSKI D., Some remarks on Kuratowski's measure of noncompactness in vector spaces with a metric, Comment. Math. Prace Mat. XXXII (1992), 5-9. (1992) Zbl0772.47031MR1202752
  7. CELLINA A., On the existence of solutions of ordinary differential equations in Banach spaces, Funkcial. Ekvac. 14 (1971), 129-136. (1971) Zbl0271.34071MR0304805
  8. CZARNOWSKI K.-PRUSZKO T., On the structure of fixed point sets of compact maps in B0 spaces with applications to integral and differential equations in unbounded domain, J. Math. Anal. Appl. 54 (1991), 151-163. (1991) MR1087965
  9. DRAGONI R.-MACKI J. WT.-NISTRI P.-ZECCA P., Solution Sets of Differential Equations in Abstract Spaces, Pitman Res. Notes Math. Ser. 342, Longman Sci. Tech., Harlow, 1996. (1996) Zbl0847.34004MR1427944
  10. HARA T.-YONEYAMA T.-SUGIE J., Continuability of solutions of perturbated differential equations, Nonlinear Anal. 8 (1984), 963-975. (1984) MR0753769
  11. HARTMAN, PH., Ordinary Differential Equations, Wiley, New York-London-Sydney, 1964. (1964) Zbl0125.32102MR0171038
  12. JANUSZEWSKI J., On the existence of continuous solutions of nonlinear integral equations in Banach spaces, Comment. Math. Prace Mat. XXX (1990), 85-92. (1990) Zbl0737.45011MR1111787
  13. KRASNOSELSKII M. A.-KREIN S. G., K teorii obyknovennych differencialnych uravnienij v Banachovych prostranstwach, Trudy Sem. Funkc. Anal. Voronezh. Univ. 2 (1956), 3-23. (Russian) (1956) MR0086191
  14. KUBÁČEK Z., On the structure of fixed point sets of some compact maps in the Frechet space, Math. Bohem. 118 (1993), 343-358. (1993) Zbl0839.47037MR1251881
  15. KUBÁČEK Z., On the structure of the solution sets of functional differential system on an unbounded interval, (Submitted). 
  16. MORALES P., Topological properties of the set of global solutions for a class of semilinear evolution equations in Banach spaces, Atti del Convegno celebrativo del 1° centario del Circolo Matematico di Palermo, Rend. Circ. Mat. Palermo (2) Suppl. 8 (1985), 379-397. (1985) MR0881416
  17. SZUFLA S., Aronszajn type theorems for diferential and integral equations in Banach spaces, In: Proceedings of the 1st Polish Symposium on Nonlinear Analysis, Wydawnictwo Uniwersytetu Lodzkiego, Lodz, 1997, pp. 113-123. (1997) 
  18. ŠEDA V.-KUBÁČEK Z., On the connectedness of the set of fixed points of a compact operator in the Frechet space C m ( [ b ) , 𝐑 n ) , Czechoslovak Math. J. 42 (117) (1992), 577-588. (1992) MR1182189
  19. WÓJTOWICZ D. (BUGAJEWSKA), On implicit Darboux problem in Banach spaces, Bull. Austral. Math. Soc. 56 (1997), 149-156. (1997) MR1464057

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