# Article

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Keywords:
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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