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Keywords:
Positive solutions; Fredholm integral equations; cone; boundary value problems; fixed point theorem.
Positive solutions; Fredholm integral equations; cone; boundary value problems; fixed point theorem.
Summary:
We study the existence of positive solutions of the integral equation \[ x(t) = \mu \int _0^1 k(t, s) f(s, x(s), x^{\prime }(s), \ldots , x^{(n-1)} (s))\, ds, \quad n \ge 2 \] in both $ C^{n-1} [0, 1] $ and $ W^{n-1, p} [0, 1] $ spaces, where $ p \ge 1 $ and $ \mu > 0 $. Throughout this paper $k$ is nonnegative but the nonlinearity $f$ may take negative values. The Krasnosielski fixed point theorem on cone is used.
References:
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