The Non Linear Cauchy Problem Of Operator Differential Equations
Marija Skendžić (1970)
Publications de l'Institut Mathématique
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Marija Skendžić (1970)
Publications de l'Institut Mathématique
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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.
Hernán R. Henríquez, Genaro Castillo G. (2003)
Annales Polonici Mathematici
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We establish existence of mild solutions for the semilinear first order functional abstract Cauchy problem and we prove that the set of mild solutions of this problem is connected in the space of continuous functions.
J. Ligęza (1975)
Colloquium Mathematicae
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James M. Irwin, Darrell C. Kent (1979)
Mathematica Slovaca
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Jan Persson (1976)
Publications mathématiques et informatique de Rennes
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Kent, Darrell C. (1984)
International Journal of Mathematics and Mathematical Sciences
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Mozgawa, Witold (2009)
Beiträge zur Algebra und Geometrie
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M. Stojanović (1974)
Matematički Vesnik
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Byszewski, L. (1993)
Journal of Applied Mathematics and Stochastic Analysis
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P. Besala (1983)
Annales Polonici Mathematici
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Rath, Nandita (2000)
International Journal of Mathematics and Mathematical Sciences
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Lowen-Colebunders, Eva (1982)
International Journal of Mathematics and Mathematical Sciences
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Raetz, Juerg (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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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.