Previous |  Up |  Next


Title: On the Volterra integral equation with weakly singular kernel (English)
Author: Szufla, Stanisław
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 131
Issue: 3
Year: 2006
Pages: 225-231
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: integral equation
Keyword: integrable solution
Keyword: measure of noncompactness
MSC: 45G05
MSC: 45N05
idZBL: Zbl 1110.45003
idMR: MR2248592
DOI: 10.21136/MB.2006.134139
Date available: 2009-09-24T22:25:59Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] N. V. Azbieliev, Z. B. Caliuk: Ob integralnych nieravienstvach.Matem. Sbornik 56 (1962), 325–342. MR 0140907
Reference: [2] J. Banaś, K. Goebel: Measure of Noncompactness in Banach Spaces.Marcel Dekker, New York, 1980. MR 0591679
Reference: [3] G. Gripenberg: Unique solutions of some Volterra integral equations.Math. Scand. 48 (1981), 59–67. Zbl 0463.45002, MR 0621417, 10.7146/math.scand.a-11899
Reference: [4] H. P. Heinz: On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions.Nonlinear Anal., Theory Methods Appl. 7 (1983), 1351–1371. Zbl 0528.47046, MR 0726478, 10.1016/0362-546X(83)90006-8
Reference: [5] J. Kurzweil: Ordinary Differential Equations.Elsevier, Amsterdam-Oxford, 1986. Zbl 0667.34002, MR 0929466
Reference: [6] H. Mönch: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces.Nonlinear Anal., Theory Methods Appl. 4 (1980), 985–999. MR 0586861, 10.1016/0362-546X(80)90010-3
Reference: [7] W. Mydlarczyk: The existence of nontrivial solutions of Volterra equations.Math. Scand. 68 (1991), 83–88. Zbl 0701.45002, MR 1124821, 10.7146/math.scand.a-12347
Reference: [8] S. Szufla: Appendix to the paper An existence theorem for the Urysohn integral equation in Banach spaces.Commentat. Math. Univ. Carol. 25 (1984), 763–764. Zbl 0578.45018, MR 0782024


Files Size Format View
MathBohem_131-2006-3_1.pdf 289.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo