A generalization of Bihari's lemma to the case of Volterra operators in Lebesgue spaces

DOI10.1134/S0001434613110114zbMath1285.47089WikidataQ124894157 ScholiaQ124894157MaRDI QIDQ2439982

A. V. Chernov

Publication date: 26 March 2014

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Lebesgue spaceVolterra operatorcontrolled functional-operator equationVolterra \(\delta\)-chainGronwall's lemmaGoursat-Darboux problemBihari's lemma

Mathematics Subject Classification ID

Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Applications of operator theory to differential and integral equations (47N20) Abstract integral equations, integral equations in abstract spaces (45N05) Matrix and operator functional equations (39B42)

Related Items

Products of composition operators and integral-type operators from Zygmund-type spaces to \(Q_K\) spaces ⋮ Non-Volterra first-order test for the preservation of solvability of a controlled Hammerstein-type equation

Cites Work

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• Pointwise estimation of the difference of the solutions of a controlled functional operator equation in Lebesgue spaces
• Weak solutions to the equations of motion of viscous compressible reacting binary mixtures: uniqueness and Lipschitz-continuous dependence on data
• Optimization of semilinear hyperbolic systems with smooth boundary controls
• Yosida approximation and nonlinear hyperbolic equation
• A generalization of a lemma of bellman and its application to uniqueness problems of differential equations
• Volterra inequalities in function spaces
• The features of gradient methods for distributed optimal-control problems