Geodesic
On the Volterra integral equation with weakly singular kernel
Mathematica Bohemica, Tome 131 (2006) no. 3, pp. 225-231

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MR Zbl
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.
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.
DOI : 10.21136/MB.2006.134139
Classification : 45G05, 45N05
Keywords: integral equation; integrable solution; measure of noncompactness 
Szufla, Stanisław. On the Volterra integral equation with weakly singular kernel. Mathematica Bohemica, Tome 131 (2006) no. 3, pp. 225-231. doi: 10.21136/MB.2006.134139
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