# On the Volterra integral equation and axiomatic measures of weak noncompactness

Mathematica Bohemica (2001)

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

## Access Full Article

top## Abstract

top## How to cite

topBugajewski, 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; nonlinear Volterra integral equation; Kneser property; 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; nonlinear Volterra integral equation; Kneser property; measure of weak noncompactness; nonlinear Volterra integral equation; Kneser property

UR - http://eudml.org/doc/248884

ER -

## References

top- Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Mat. Univ. Padova 39 (1967), 349–360. (1967) MR0222426
- 10.1007/BF01762795, Ann. Mat. Pura Appl. 151 (1988), 213–224. (1988) MR0964510DOI10.1007/BF01762795
- On the existence of weak solutions of integral equations in Banach spaces, Comment. Math. Univ. Carolin. 35 (1994), 35–41. (1994) MR1292580
- 10.1016/0362-546X(93)90015-K, Nonlinear Anal. 20 (1993), 169–173. (1993) MR1200387DOI10.1016/0362-546X(93)90015-K
- 10.1016/0362-546X(78)90063-9, Nonlinear Anal. 2 (1978), 169–177. (1978) MR0512280DOI10.1016/0362-546X(78)90063-9
- On a property of the unit sphere in Banach spaces, Bull. Math. Soc. Sci. Math. Roum. 21 (1977), 259–262. (1977) MR0482402
- Measures of weak noncompactness and fixed point theorems, Bull. Math. Soc. Sci. Math. Roum. 25 (1981), 353–358. (1981)
- Linear Topological Spaces, Van Nostrand, Princeton, 1963. (1963) MR0166578
- To the theory of ordinary differential equations in Banach spaces, Trudy Sem. Funk. Anal. Voronezh. Univ. 2 (1956), 3–23. (Russian) (1956) MR0086191
- 10.1090/S0002-9939-96-03154-1, Proc. Amer. Math. Soc. 124 (1996), 607–614. (1996) MR1301043DOI10.1090/S0002-9939-96-03154-1
- Existence theorem for weak solutions of ordinary differential equations in reflexive Banach spaces, Studia Sci. Math. Hungarica 6 (1971), 197–203. (1971) MR0330688

## NotesEmbed ?

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