Geodesic
Pointwise Estimation of the Difference of the Solutions of a Controlled Functional Operator Equation in Lebesgue Spaces
Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 288-302 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a functional operator equation in Lebesgue space, we prove a statement on the pointwise estimate of the modulus of the increment of its global (on a fixed set $\Pi\subset\mathbb R^n$) solution under the variation of the control function appearing in this equation. As an auxiliary statement, we prove a generalization of Gronwall's lemma to the case of a nonlinear operator acting in Lebesgue space. The approach used here is based on methods from the theory of stability of existence of global solutions to Volterra operator equations.
Keywords: functional operator equation, control function, initial boundary-value problem, Gronwall's lemma, Volterra operator equation
Mots-clés : Lebesgue space, increment of a solution. 
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A. V. Chernov. Pointwise Estimation of the Difference of the Solutions of a Controlled Functional Operator Equation in Lebesgue Spaces. Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 288-302. http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a10/

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