Differential equations in banach space and henstock-kurzweil integrals

Ireneusz Kubiaczyk; Aneta Sikorska

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1999)

  • Volume: 19, Issue: 1-2, page 35-43
  • ISSN: 1509-9407

Abstract

top
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.

How to cite

top

Ireneusz Kubiaczyk, and Aneta Sikorska. "Differential equations in banach space and henstock-kurzweil integrals." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 19.1-2 (1999): 35-43. <http://eudml.org/doc/275964>.

@article{IreneuszKubiaczyk1999,
abstract = {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.},
author = {Ireneusz Kubiaczyk, Aneta Sikorska},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Cauchy problem; existence of solution; Henstock-Kurzweil integral; Henstock-Kurzweil integrals; existence; solutions; abstract differential inclusions},
language = {eng},
number = {1-2},
pages = {35-43},
title = {Differential equations in banach space and henstock-kurzweil integrals},
url = {http://eudml.org/doc/275964},
volume = {19},
year = {1999},
}

TY - JOUR
AU - Ireneusz Kubiaczyk
AU - Aneta Sikorska
TI - Differential equations in banach space and henstock-kurzweil integrals
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1999
VL - 19
IS - 1-2
SP - 35
EP - 43
AB - 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.
LA - eng
KW - Cauchy problem; existence of solution; Henstock-Kurzweil integral; Henstock-Kurzweil integrals; existence; solutions; abstract differential inclusions
UR - http://eudml.org/doc/275964
ER -

References

top
  1. [1] A. Ambrosetti, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Univ. Padova 39 (1967), 349-360. 
  2. [2] Z. Artstein, Topological dynamics of ordinary differential equations and Kurzweil, equations, J. Differential Equations 23 (1977), 224-243. Zbl0353.34044
  3. [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. Zbl0441.47056
  4. [4] S.S. Cao, The Henstock integral for Banach valued functions, SEA Bull. Math. 16 (1992), 36-40. 
  5. [5] T.S. Chew, On Kurzweil generalized ordinary differential equations, J. Differential Equations 76 (1988), 286-293. Zbl0666.34041
  6. [6] T.S. Chew and F. Flovdelija, On x' = f(t,x) and Henstock-Kurzweil integrals, Differential and Integral Equations 4 (1991), 861-868. Zbl0733.34004
  7. [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). Zbl0202.10003
  8. [8] R.A. Gordon, The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Providence, Rhode Island 1994. Zbl0807.26004
  9. [9] P. Hartman, Ordinary Differential Equations, New York 1964. Zbl0125.32102
  10. [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. Zbl0528.47046
  11. [11] R. Henstock, The General Theory of Integration, Oxford Mathematical Monographs, Clavendon Press, Oxford 1991. Zbl0745.26006
  12. [12] H. Mönch, Boundary value problems for nonlinear differential equations of second order in Banach spaces, Nonlinear Analysis 4 (1980), 985-999. Zbl0462.34041
  13. [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. Zbl0927.26011
  14. [14] S. Schwabik, Generalized Ordinary Differential Equations, World Scientific, Singapore 1992. Zbl0781.34003

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.