On the application of measure of noncompactness to existence theorems

Stanisław Szufla

Rendiconti del Seminario Matematico della Università di Padova (1986)

  • Volume: 75, page 1-14
  • ISSN: 0041-8994

How to cite

top

Szufla, Stanisław. "On the application of measure of noncompactness to existence theorems." Rendiconti del Seminario Matematico della Università di Padova 75 (1986): 1-14. <http://eudml.org/doc/108021>.

@article{Szufla1986,
author = {Szufla, Stanisław},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {measure of noncompactness; Hammerstein; quasilinear evolution equations; Banach space; continuous solution},
language = {eng},
pages = {1-14},
publisher = {Seminario Matematico of the University of Padua},
title = {On the application of measure of noncompactness to existence theorems},
url = {http://eudml.org/doc/108021},
volume = {75},
year = {1986},
}

TY - JOUR
AU - Szufla, Stanisław
TI - On the application of measure of noncompactness to existence theorems
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1986
PB - Seminario Matematico of the University of Padua
VL - 75
SP - 1
EP - 14
LA - eng
KW - measure of noncompactness; Hammerstein; quasilinear evolution equations; Banach space; continuous solution
UR - http://eudml.org/doc/108021
ER -

References

top
  1. [1] A. Ambrosetti, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Semin. Mat. Univ. Padova, 39 (1967), pp. 349-360. Zbl0174.46001MR222426
  2. [2] F. Browder, Nonlinear equations of evolution, Ann. of Math., 80 (1964), pp. 485-523. Zbl0127.33602MR173960
  3. [3] F. Browder, Nonlinear operators and nonlinear equations of evolution, Proc. Symp. Nonlin. Funct. Anal. Chicago, AMS, 20 II, Providence, R. I., 1972. 
  4. [4] A. Cellina, On the existence of solutions of ordinary differential equations in Banach spaces, Funkcial. Ekvac., 14 (1971), pp. 129-136. Zbl0271.34071MR304805
  5. [5] J. Chandra - V. LAKSHMIKANTHAM - A. MITCHELL, Existence of solutions of boundary value problems for nonlinear second order systems in a Banach space, J. Nonlinear Anal., 2 (1978), pp. 157-168. Zbl0385.34035MR512279
  6. [6] J. Daneš, On densifying and related mappings and their applications in nonlinear functional analysis, Theory of nonlinear operators, Akademie-Verlag, Berlin (1974), pp. 15-56. Zbl0295.47058MR361946
  7. [7] G. Darbo, Punti uniti in trasformazioni a condominio non compatto, Rend. Sem. Mat. Univ. Padova, 24 (1955), pp. 84-92. Zbl0064.35704MR70164
  8. [8] K. Deimling, Ordinary differential equations in Banach spaces, Lecture Notes Math. no. 596, Berlin, Heidelberg, New York, 1977. Zbl0361.34050MR463601
  9. [9] K. Goebel - W. Rzymowski, An existence theorem for the equation x' = f (t, x) in Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 18 (1970), pp. 367-370. Zbl0202.10003MR269957
  10. [10] P. Hartman, Ordinary differential equations, New York, London, Sydney, 1964. Zbl0125.32102MR171038
  11. [11] A. Koschelev - M. Krasnoselskii - S. Michlin - L. Rakovschik- V. Stecenko - P. Zabreiko, Integral equations, SMB, Moskva, 1968. 
  12. [12] K. Kuratowski, Topologie, Warszawa, 1958. Zbl0078.14603
  13. [13] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, J. Nonlinear Anal., 4 (1980), pp. 985-999. Zbl0462.34041MR586861
  14. [14] G. Pianigiani, Existence of solutions of ordinary differential equations in Banach spaces, Bull. Acad. Pelon. Sci. Sér. Sci. Math. Astronom. Phys., 23 (1975), pp. 853-857. Zbl0317.34050MR393710
  15. [15] J Prüß, On semilinear evolution equations in Banach spaces, J. Reine Angew Math., 303-304 (1978), pp. 144-158. Zbl0398.34057MR514677
  16. [16] B. Sadovskii, On a fixed point principle, Frunkcjcnalnyj Analiz., 1 (1976), pp. 74-76. Zbl0165.49102MR211302
  17. [17] G. Scorza-Dragoni, Sul problema dei valori ai limiti per i sistemi di equazioni differenziali del secondo ordine, Bcll. U.M.I., 14 (1935), pp. 225-230. Zbl61.1238.08JFM61.1238.08
  18. [18] S. Szufla, Some remarks on ordinary differential equations in Banach spaces, Bull. Acad. Pclon. Sci. Sθr. Sci. Math. Astronom. Phys., 16 (1968), pp. 795-800. Zbl0177.18902
  19. [19] S. Szufla, Równania różniczkowe w przestrzeniach Banacha, Ph. D. Thesis, Poznań, 1972. 
  20. [20] S. Szufla, On the existence of solutions of differential equations in Banach spaces, Bull. Acad. Polon. Sci. Math., 30 (1982), pp. 507-515. Zbl0532.34045MR718727
  21. [21] S. Szufla, On Volterra integral equations in Banach spaces, Funkcial. Ekvac., 20 (1977), pp. 247-258. Zbl0379.45025MR511230

Citations in EuDML Documents

top
  1. Mieczysław Cichoń, Ireneusz Kubiaczyk, Existence theorem for the Hammerstein integral equation
  2. Djamila Seba, Nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in Banach spaces
  3. Dariusz Bugajewski, On the existence of weak solutions of integral equations in Banach spaces
  4. Dariusz Bugajewski, On fixed point theorems for absolute retracts
  5. Afif Ben Amar, Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability

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.