Absolutely continuous solutions of Cauchy's problem for \(u_{xy} = f(x,y,u,u_ x,u_ y)\)

DOI10.1007/BF02414955zbMath0223.35056MaRDI QIDQ2548030

Klaus Deimling

Publication date: 1971

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15)

Related Items (7)

On the Cauchy problem for linear hyperbolic functional-differential equations ⋮ Linear hyperbolic functional-differential equations with essentially bounded right-hand side ⋮ Carathéodory solutions to a hyperbolic differential inequality with a non-positive coefficient and delayed arguments ⋮ Nonnegative solutions of the characteristic initial value problem for linear partial functional-differential equations of hyperbolic type ⋮ Unique solvability of the Darboux problem for linear hyperbolic functional differential equations ⋮ Some remarks on linear functional differential inequalities of hyperbolic type ⋮ Noncompact-type Krasnoselskii fixed-point theorems and their applications

Cites Work

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• Eine Bemerkung über hyperbolische Systeme partieller Differentialgleichungen zweiter Ordnung
• Das Picard-Problem für \(u_{xy} = f(x,y,u,u_ x,u_ y)\) unter Caratheodory-Voraussetzungen
• A Carathéodory theory for systems of integral equations
• Remarque sur la régularité des intégrales des équations différentielles hyperboliques du second ordre
• Differential- und Integral-Ungleichungen
• On Hyperbolic Partial Differential Equations

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