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1999 | 19 | 1-2 | 35-43
Tytuł artykułu

Differential equations in banach space and henstock-kurzweil integrals

Warianty tytułu
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EN
Abstrakty
EN
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.
Twórcy
  • 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
  • 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
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