Geodesic
Existence Theorems for Lp - Solutions of Integral Equations in Banach Spaces
Publications de l'Institut Mathématique, _N_S_40 (1986) no. 54, p. 99

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We study the integral equation $x=F(x)$ in a Banach space $E$, where $F(x)(t)=\int_Df(t,s,x(s))ds$ and $f$ satisfies usual conditions which guarantee that $F$ continuously maps the space $L^P(D,E)$ into itself. We show that if $f$ satisfies a Kamke condition with respect to the Kuratowski measure of noncompactness, then the above equation has a solution in $L^P(D,E)$.
Classification : 45N05 
@article{PIM_1986_N_S_40_54_a10,
     author = {Stanislaw Szufla},
     title = {Existence {Theorems} for {Lp} - {Solutions} of {Integral} {Equations} in {Banach} {Spaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {99 },
     publisher = {mathdoc},
     volume = {_N_S_40},
     number = {54},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1986_N_S_40_54_a10/}
}
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Stanislaw Szufla. Existence Theorems for Lp - Solutions of Integral Equations in Banach Spaces. Publications de l'Institut Mathématique, _N_S_40 (1986) no. 54, p. 99 . http://geodesic.mathdoc.fr/item/PIM_1986_N_S_40_54_a10/