The existence of bounded solutions for differential equations in Hilbert spaces

• Autorzy: B. Przeradzki
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991-1992
• Tom: 56
• Numer: 2
• Strony: 103-121

Daty

wydano

1992

otrzymano

1989-10-18

poprawiono

1990-03-19

Twórcy

autor

B. Przeradzki

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

Bibliografia

• [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.