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Mat. Zametki, 2004, Volume 76, Issue 1, Pages 11–19 (Mi mz84)  

The Wiener–Hopf Integral Equation in the Supercritical Case

L. G. Arabadzhyan

Armenian State Teachers' Training University named after Khachatur Abovian

Abstract: We consider the scalar homogeneous equation
$$ S(x)=\int_0^\infty K(x-t)S(t) dt, \qquad x\in\mathbb R^+\equiv(0,\infty), $$
with symmetric kernel $K$: $K(-x)=K(x)$, $x\in\mathbb R_1$ satisfying the conditions
$$ 0\leqslant K\in L_1(\mathbb R^+)\cap C^{(2)}(\mathbb R^+), \qquad \int_0^\infty K(t) dt>\frac12, $$
$K'\leqslant 0$ and $0\leqslant K"\downarrow$ on $\mathbb R^+$. We prove the existence of a real solution $S$ of the equation given above with asymptotic behavior $S(x)=O(x)$ as $x\to+\infty$.

DOI: https://doi.org/10.4213/mzm84

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English version:
Mathematical Notes, 2004, 76:1, 10–17

Bibliographic databases:

UDC: 517.9
Received: 28.08.2000
Revised: 12.09.2003

Citation: L. G. Arabadzhyan, “The Wiener–Hopf Integral Equation in the Supercritical Case”, Mat. Zametki, 76:1 (2004), 11–19; Math. Notes, 76:1 (2004), 10–17

Citation in format AMSBIB
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