On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments

Antoni Augustynowicz

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Displaying similar documents to “On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments”

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Journées équations aux dérivées partielles

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We shall give the local in time existence of the solutions in Gevrey classes to the Cauchy problem for Kirhhoff equations of $p$ -laplacian type and investigate the propagation of analyticity of solutions for real analytic deta. When $p = 2$ , his equation as the global real analytic solution for the real analytic initial data.

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H. Marcinkowska (1971)

Annales Polonici Mathematici

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Counterexamples to Hölmgren's uniqueness for analytic non linear Cauchy problem.

G. Métivier (1993)

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Michael Christ (1990)

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Abstract differential inequalities and the Cauchy problem for infinite-dimensional linear functional differential equations.

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On the Cauchy problem for linear PDEs with retarded arguments at derivatives

Krzysztof A. Topolski (2015)

Annales Polonici Mathematici

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We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.

Cauchy's problem for systems of linear differential equations with distributional coefficients

J. Ligęza (1975)

Colloquium Mathematicae

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The Cauchy problem for the system of partial differential equations describing nonsimple thermoelasticity

Henryk Kołakowski, Jarosław Łazuka (2008)

Applicationes Mathematicae

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The aim of this paper is to derive a formula for the solution to the Cauchy problem for the linear system of partial differential equations describing nonsimple thermoelasticity. Some properties of the solution are also presented. It is a first step to study the nonlinear case.

The Non Linear Cauchy Problem Of Operator Differential Equations

Marija Skendžić (1970)

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Nonanalytic solutions of the KdV equation.

Byers, Peter, Himonas, A.Alexandrou (2004)

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An analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function

Mitja Nedic (2023)

Czechoslovak Mathematical Journal

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We derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula satisfied by Herglotz-Nevanlinna and Cauchy-type functions. We also provide an extension of the Stieltjes inversion formula for Cauchy-type and quasi-Cauchy-type functions.