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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 2, 2002, pp. 381–398
DOI: 10.4171/ZAA/1084

Published online: 2002-06-30

On the Solutions of a Quadratic Integral and an Integral-Differential Equation

Lothar von Wolfersdorf

An integral equation and a related integral-differential equation of first order over $\mathbb R_+$ with a quadratic integral term representing the so-called autocorrelation of the unknown function is dealt with. For both equations the general solution is constructed and estimated in the $L^2$-norm. Further, the asymptotic behaviour and the stability of the solution are investigated.

Keywords: Nonlinear integral equations, nonlinear integro-ordinary differential equations, boundary value problems for holomorphic functions

von Wolfersdorf Lothar: On the Solutions of a Quadratic Integral and an Integral-Differential Equation. Z. Anal. Anwend. 21 (2002), 381-398. doi: 10.4171/ZAA/1084