The existence of bounded solutions for differential equations in Hilbert spaces

B. Przeradzki

Annales Polonici Mathematici (1992)

  • Volume: 56, Issue: 2, page 103-121
  • ISSN: 0066-2216

Abstract

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The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.

How to cite

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B. Przeradzki. "The existence of bounded solutions for differential equations in Hilbert spaces." Annales Polonici Mathematici 56.2 (1992): 103-121. <http://eudml.org/doc/262254>.

@article{B1992,
abstract = {The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.},
author = {B. Przeradzki},
journal = {Annales Polonici Mathematici},
keywords = {bounded solutions; exponentially dichotomic; condensing; measure of non- compactness},
language = {eng},
number = {2},
pages = {103-121},
title = {The existence of bounded solutions for differential equations in Hilbert spaces},
url = {http://eudml.org/doc/262254},
volume = {56},
year = {1992},
}

TY - JOUR
AU - B. Przeradzki
TI - The existence of bounded solutions for differential equations in Hilbert spaces
JO - Annales Polonici Mathematici
PY - 1992
VL - 56
IS - 2
SP - 103
EP - 121
AB - The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.
LA - eng
KW - bounded solutions; exponentially dichotomic; condensing; measure of non- compactness
UR - http://eudml.org/doc/262254
ER -

References

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  1. [1] Yu. L. Daletskiĭ and M. G. Kreĭn, Stability of Solutions of Differential Equations in a Banach Space, Nauka, Moscow 1970 (in Russian). 
  2. [2] K. Goebel and W. Rzymowski, An existence theorem for the equations x' = f(x,t) in Banach spaces, Bull. Acad. Polon. Sci. 18 (7) (1970), 367-370. Zbl0202.10003
  3. [3] K. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301-309. Zbl56.1124.04
  4. [4] J. Massera and J. Schäffer, Linear Differential Equations and Function Spaces, Acad. Press, New York and London 1966. Zbl0243.34107
  5. [5] B. N. Sadovskiĭ, Ultimately compact and condensing operators, Uspekhi Mat. Nauk 27 (1) (1972), 82-146 (in Russian). 
  6. [6] T. Ważewski, Sur la limitation des intégrales des systèmes d'équations différentielles linéaires ordinaires, Studia Math. 10 (1948), 48-59. Zbl0036.05703

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