On the structure of solution set of an integro-differential equation in Banach spaces

• Autorzy: Roszak M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we shall present two existence theorems for local solutions of an initial value problem for nonlinear integro-differential equation in a Banach space.

Słowa kluczowe

EN

Banach space; initial boundary value problems; differential equations; measure of noncompactness

PL

równania różniczkowe; zagadnienia brzegowe; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 341--348
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Roszak M.

• Faculty of Computing Science, The Institution of Higher Learning for Humanities and Journalism, ul. Kutrzeby 10, 61-719 Poznań, Poland

Bibliografia

• [1] N. Aronszajn, Le correspondant topologique de l'unicite dans la théorie des equations différentielles, Ann. Math. 43 (1942), 730-738.
• [2] J. Banaś, K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math. 60, Marcel Dekker, New York and Basel 1980.
• [3] H. P. Heinz, On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions, Nonlin. Anal. Theory Math. Appl. 7 (1983), 1351-1371.
• [4] C. Olech, On the existence and uniqueness of solution of an ordinary differential equation in the case of Banach space, Bull. Acad. Polon. Sci. Math. 8 (1960), 667-673.
• [5] J. Szmyd, S. Szufla, On the Aronszajn property for an integro-differential equation in Banach spaces, Demonstratio Math. 30 (1997), 671-678.
• [6] S. Szufla, On the existence of solutions of an ordinary differential equation in the case of Banach spaces, Bull. Acad. Polon. Sci. Math. 16 (1968), 311-315.
• [7] S. Szufla, Some remarks on ordinary differential equations in Banach spaces, ibid., 16 (1968), 795-800.
• [8] S. Szufla, Solutions sets of nonlinear equations, ibid., 21 (1973), 971-976.
• [9] G. Vidossich, On the structure of solutions set of nonlinear equations, J. Math. Anal. Appl., 34 (1971), 602-617.
• [10] G. Vidossich, A fixed point theorem for function spaces, ibid., 36 (1971), 581-587.