ArticleOriginal scientific text

Title

The existence of bounded solutions for differential equations in Hilbert spaces

Authors 1

Affiliations

  1. Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

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.

Bibliography

  1. Yu. L. Daletskiĭ and M. G. Kreĭn, Stability of Solutions of Differential Equations in a Banach Space, Nauka, Moscow 1970 (in Russian).
  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.
  3. K. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301-309.
  4. J. Massera and J. Schäffer, Linear Differential Equations and Function Spaces, Acad. Press, New York and London 1966.
  5. B. N. Sadovskiĭ, Ultimately compact and condensing operators, Uspekhi Mat. Nauk 27 (1) (1972), 82-146 (in Russian).
  6. T. Ważewski, Sur la limitation des intégrales des systèmes d'équations différentielles linéaires ordinaires, Studia Math. 10 (1948), 48-59.
Pages:
103-121
Main language of publication
English
Received
1989-10-18
Accepted
1990-03-19
Published
1992
Exact and natural sciences