Warianty tytułu
Języki publikacji
Abstrakty
In this paper, using the properties of the Henstock-Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x' = f(t,x) and inclusion x' ∈ F(t,x) in a Banach space, where f is Henstock-Kurzweil integrable and satisfies some conditions.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
35-43
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-04-21
Twórcy
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
- Institute of Mathematics, Technical University, Podgórna 50, 65-246 Zielona Góra, Poland
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
Bibliografia
- [1] A. Ambrosetti, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Univ. Padova 39 (1967), 349-360.
- [2] Z. Artstein, Topological dynamics of ordinary differential equations and Kurzweil, equations, J. Differential Equations 23 (1977), 224-243.
- [3] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math., Mercel Dekker 60 (1980), New York and Basel.
- [4] S.S. Cao, The Henstock integral for Banach valued functions, SEA Bull. Math. 16 (1992), 36-40.
- [5] T.S. Chew, On Kurzweil generalized ordinary differential equations, J. Differential Equations 76 (1988), 286-293.
- [6] T.S. Chew and F. Flovdelija, On x' = f(t,x) and Henstock-Kurzweil integrals, Differential and Integral Equations 4 (1991), 861-868.
- [7] K. Goebel and W. Rzymowski, An existence theorem for the equations x' = f(t,x) in Banach space, Bulletin de l'Academie Polonaise des Sciences 7 (1970).
- [8] R.A. Gordon, The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Providence, Rhode Island 1994.
- [9] P. Hartman, Ordinary Differential Equations, New York 1964.
- [10] H.P. Heinz, On the behaviour of measures of noncompactness with respect to differentation and integration of vector-valued functions, Nonlinear Anal. 7 (1983), 1351-1371.
- [11] R. Henstock, The General Theory of Integration, Oxford Mathematical Monographs, Clavendon Press, Oxford 1991.
- [12] H. Mönch, Boundary value problems for nonlinear differential equations of second order in Banach spaces, Nonlinear Analysis 4 (1980), 985-999.
- [13] S. Nakanishi, The Henstock integral for functions with values in nuclear spaces and the Henstock lemma, Journal of Mathematical Study 27 (1994), 133-141.
- [14] S. Schwabik, Generalized Ordinary Differential Equations, World Scientific, Singapore 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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