An existence theorem for solutions of an integro-differential equation in Banach spaces

• Autorzy: Dutkiewicz A.
• Języki publikacji: EN

Abstrakty

EN

The paper contains an existence theorem for local solutions of an initial value problem for a nonlinear integro-differential equation in Banach spaces. The assumptions and proofs are expressed in terms of measures of noncompactness.

Słowa kluczowe

EN

integro-differential equation; Cauchy problem; measure of noncompactness

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 4
• Strony: 895--899
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Dutkiewicz A.

• Faculty Of Mathematics And Computer Science A.Mickiewicz University Umultowska 87 61 614 Poznań, Poland,

Bibliografia

• [1] J.Banaś, K.Goebel, Measures of Noncompactness in Banach Spaces Marcel Dekker, New York Basel, 1980.
• [2] H.P.Heinz, On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions Nonlinear Anal.7 (1983), 1351–1371.
• [3] S.Szufla, On Volterra integral equations in Banach spaces Funkcial. Ekvac.20 (1977), 247–258.
• [4] S.Szufla, Osgood type conditions for an m-th order differential equation Discuss. Math. Differential. Incl.18 (1998), 45–55.
• [5] S.Szufla, On the differential equation x (m)= f(t, x) in Banach spaces Funkcial. Ekvac.41 (1998), 101–105.
• [6] S.Szufla, A.Szukała, Aronszajn type theorems for an mth order differential equation in Banach spaces Funct.Approx.27 (1999), 99–108.
• [7] G.Vidossich, A fixed point theorem for function spaces J.Math. Anal. Appl. 36 (1971), 581–587.