On the equation y ' = f ( t , y ) in Banach spaces

Bogdan Rzepecki

Commentationes Mathematicae Universitatis Carolinae (1983)

  • Volume: 024, Issue: 4, page 609-630
  • ISSN: 0010-2628

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Rzepecki, Bogdan. "On the equation $y^{\prime }=f(t,y)$ in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 024.4 (1983): 609-630. <http://eudml.org/doc/17281>.

@article{Rzepecki1983,
author = {Rzepecki, Bogdan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Banach spaces; structure of the set of solutions; measure of noncompactness; Euler polygonals; extremal solutions},
language = {eng},
number = {4},
pages = {609-630},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the equation $y^\{\prime \}=f(t,y)$ in Banach spaces},
url = {http://eudml.org/doc/17281},
volume = {024},
year = {1983},
}

TY - JOUR
AU - Rzepecki, Bogdan
TI - On the equation $y^{\prime }=f(t,y)$ in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1983
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 024
IS - 4
SP - 609
EP - 630
LA - eng
KW - Banach spaces; structure of the set of solutions; measure of noncompactness; Euler polygonals; extremal solutions
UR - http://eudml.org/doc/17281
ER -

References

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  2. J. BANAŚ K. GOEBEL, Measure of noncompactness in Banach spaces, Lect. Notes Pure Applied Math. 60, Marcel Dekker, New York 1980. (1980) MR0591679
  3. J. BANAŚ A. HAJHOSZ S. WEDRYCHOWICZ, Some generalization of Szufla's theorem for ordinary differential equations in Banach space, Bull. Acad. Polon. Sci., Sér. Sci. Math. 29 (1981), 459-464. (1981) MR0646334
  4. J. DANEŠ, Some fixed point theorems, Comment. Math. Univ. Carolinae 9 (1968), 223-235. (1968) MR0235435
  5. J. DANEŠ, On denslfying and related mappings and their application in nonlinear functional analysis, Theory of nonlinear operators, Akademie-Verlag, Berlin 1974, 15-56. (1974) MR0361946
  6. K. DEIMLING, Ordinary differential equations in Banach spaces, Lect. Notes in Math. 596, Springer-Verlag, Berlin 1977. (1977) Zbl0361.34050MR0463601
  7. K. GOEBEL W. RZYMOWSKI, An existence theorem for the equation x ' = f ( t , x ) in Banach space, Bull. Acad. Polon. Sol., Sér. Sol. Math. Astronom. Phys. 28 (1970), 367-370. (1970) MR0269957
  8. M. A. KPACHOCEЛЬCKИЙ C. Г. KPEЙH, O npинсипe ycpeднения в нeлинейной механике, Ycnexн Mат. Hayx 10 (1955), 147-152. (1955) 
  9. K. KURATOWSKI, Sur les espaces complete, Fund. Math. 15 (1930), 301-309. (1930) 
  10. V. LAKSHMIKANTHAM S. LEELA, Differential and integral inequalities, Vol. 1, Academic Press, New York 1969. (1969) 
  11. B. RZEPECKI, On the operator equation in Banach spaces, Demonstratio Math. 12 (1979), 189-201. (1979) Zbl0421.47034MR0542317
  12. B. RZEPECKI, Some properties of the set of solutions on an operator equation in a Banach space, Comment. Math. 22 (1978), 467-478. (1978) MR0519385
  13. B. RZEPECKI, On measure of noncompactness in topological spaces, Comment. Math. Univ. Carolinae 23 (1982), 105-116. (1982) MR0653354
  14. B. RZEPECKI, Euler polygons and Kneser's theorem for solutions of differential equations in Banach spaces, Comment. Math. Univ. Carolinae 23 (1982), 657-669. (1982) Zbl0517.34049MR0687561
  15. B. N. SADOVSKII, Limit compact and condensing operators, Russian Math. Surveys 27 (1972), 86-144. (1972) MR0428132
  16. A. STOKES, The application of a fixed-point theorem to a variety of nonlinear stability problems, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 231-235. (1959) MR0104006
  17. J. SZARSKI, Differential inequalities, PWN, Warszawa 1965. (1965) Zbl0135.25804MR0190409
  18. S. SZUFLA, Some remarks on ordinary differential equations in Banach spaces, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Pnys. 16 (1968), 795-800. (1968) Zbl0177.18902MR0239238
  19. S. SZUFLA, Solutions sets of nonlinear equations, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Pnys. 21 (1973), 971-976. (1973) Zbl0272.34086MR0344959
  20. S. SZUFLA, Some properties of the solutions set of ordinary differential equations, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Pnys. 22 (1974), 675-678. (1974) Zbl0289.34096MR0355245
  21. S. SZUFLA, Kneser's theorem for weak solutions of ordinary differential equations in reflexive Banach spaces, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 26 (1978), 407-413. (1978) Zbl0384.34039MR0492684

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