PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 40(54), pp. 99--105 (1986)
EXISTENCE THEOREMS FOR $L^p$ -- SOLUTIONS OF INTEGRAL EQUATIONS IN BANACH SPACES
Stanislaw SzuflaA. Mickiewicz University, Poznan, Poland
Abstract: 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 (MSC2000): 45N05
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