Existence of positive solutions of some integral equations
Abstract
We study the existence of positive solutions of the integral equation
x(t) = ∫01k(t,s)f(s,x(s),x'{s),...,x(n-1)(s))ds, n≥2
in both Cn-1[0,1] and Wn-1,p[0,1] spaces, where p≥1. The Krasnosielskii fixed point theorem on cone is used.
Keywords
boundary value problems; positive solutions; Fredholm integral equations; cone; fixed point theorem
References
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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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