On the Volterra integral equation with weakly singular kernel

Stanisław Szufla

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 3, page 225-231
  • ISSN: 0862-7959

Abstract

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We give sufficient conditions for the existence of at least one integrable solution of equation x ( t ) = f ( t ) + ∫ 0 t K ( t , s ) g ( s , x ( s ) ) d s . Our assumptions and proofs are expressed in terms of measures of noncompactness.

How to cite

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Szufla, Stanisław. "On the Volterra integral equation with weakly singular kernel." Mathematica Bohemica 131.3 (2006): 225-231. <http://eudml.org/doc/249910>.

@article{Szufla2006,
abstract = {We give sufficient conditions for the existence of at least one integrable solution of equation $x(t)=f(t)+\int _\{0\}^\{t\} K(t,s)g(s,x(s))\mathrm \{d\}s$. Our assumptions and proofs are expressed in terms of measures of noncompactness.},
author = {Szufla, Stanisław},
journal = {Mathematica Bohemica},
keywords = {integral equation; integrable solution; measure of noncompactness; integrable solution; measure of noncompactness},
language = {eng},
number = {3},
pages = {225-231},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Volterra integral equation with weakly singular kernel},
url = {http://eudml.org/doc/249910},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Szufla, Stanisław
TI - On the Volterra integral equation with weakly singular kernel
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 3
SP - 225
EP - 231
AB - We give sufficient conditions for the existence of at least one integrable solution of equation $x(t)=f(t)+\int _{0}^{t} K(t,s)g(s,x(s))\mathrm {d}s$. Our assumptions and proofs are expressed in terms of measures of noncompactness.
LA - eng
KW - integral equation; integrable solution; measure of noncompactness; integrable solution; measure of noncompactness
UR - http://eudml.org/doc/249910
ER -

References

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  2. Measure of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980. (1980) MR0591679
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  5. Ordinary Differential Equations, Elsevier, Amsterdam-Oxford, 1986. (1986) Zbl0667.34002MR0929466
  6. 10.1016/0362-546X(80)90010-3, Nonlinear Anal., Theory Methods Appl. 4 (1980), 985–999. (1980) MR0586861DOI10.1016/0362-546X(80)90010-3
  7. 10.7146/math.scand.a-12347, Math. Scand. 68 (1991), 83–88. (1991) Zbl0701.45002MR1124821DOI10.7146/math.scand.a-12347
  8. Appendix to the paper An existence theorem for the Urysohn integral equation in Banach spaces, Commentat. Math. Univ. Carol. 25 (1984), 763–764. (1984) Zbl0578.45018MR0782024

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