On the Volterra integral equation and axiomatic measures of weak noncompactness

Dariusz Bugajewski

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 183-190
  • ISSN: 0862-7959

Abstract

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We prove that a set of weak solutions of the nonlinear Volterra integral equation has the Kneser property. The main condition in our result is formulated in terms of axiomatic measures of weak noncompactness.

How to cite

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Bugajewski, Dariusz. "On the Volterra integral equation and axiomatic measures of weak noncompactness." Mathematica Bohemica 126.1 (2001): 183-190. <http://eudml.org/doc/248884>.

@article{Bugajewski2001,
abstract = {We prove that a set of weak solutions of the nonlinear Volterra integral equation has the Kneser property. The main condition in our result is formulated in terms of axiomatic measures of weak noncompactness.},
author = {Bugajewski, Dariusz},
journal = {Mathematica Bohemica},
keywords = {measure of weak noncompactness; Volterra integral equation; measure of weak noncompactness; nonlinear Volterra integral equation; Kneser property},
language = {eng},
number = {1},
pages = {183-190},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Volterra integral equation and axiomatic measures of weak noncompactness},
url = {http://eudml.org/doc/248884},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Bugajewski, Dariusz
TI - On the Volterra integral equation and axiomatic measures of weak noncompactness
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 183
EP - 190
AB - We prove that a set of weak solutions of the nonlinear Volterra integral equation has the Kneser property. The main condition in our result is formulated in terms of axiomatic measures of weak noncompactness.
LA - eng
KW - measure of weak noncompactness; Volterra integral equation; measure of weak noncompactness; nonlinear Volterra integral equation; Kneser property
UR - http://eudml.org/doc/248884
ER -

References

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  7. Measures of weak noncompactness and fixed point theorems, Bull. Math. Soc. Sci. Math. Roum. 25 (1981), 353–358. (1981) 
  8. Linear Topological Spaces, Van Nostrand, Princeton, 1963. (1963) MR0166578
  9. To the theory of ordinary differential equations in Banach spaces, Trudy Sem. Funk. Anal. Voronezh. Univ. 2 (1956), 3–23. (Russian) (1956) MR0086191
  10. Integral equations in reflexive Banach spaces and weak topologies, Proc. Amer. Math. Soc. 124 (1996), 607–614. (1996) MR1301043
  11. Existence theorem for weak solutions of ordinary differential equations in reflexive Banach spaces, Studia Sci. Math. Hungarica 6 (1971), 197–203. (1971) MR0330688

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