Hernán R. Henríquez, Eduardo Hernández M. (2006)
Annales Polonici Mathematici
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We establish the existence of mild, strong, classical solutions for a class of second order abstract functional differential equations with nonlocal conditions.
Byszewski, Ludwik, Akca, Haydar (1997)
Journal of Applied Mathematics and Stochastic Analysis
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Byszewski, L. (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Byszewski, Ludwik (1999)
Journal of Applied Mathematics and Stochastic Analysis
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Pl. Kannappan, M. Kuczma (1974)
Annales Polonici Mathematici
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Józef Myjak
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CONTENTSIntroduction.....................................................................................................................................5 1. General results.........................................................................................................................7 1.1. Residual sets.........................................................................................................................7 1.2. Generic properties of abstract functional equations..............................................................8II....
Z. Kamont (1977)
Annales Polonici Mathematici
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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.
Józef Tabor (1975)
Colloquium Mathematicae
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Marek Kuczma (1973)
Colloquium Mathematicae
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Elżbieta Puźniakowska-Gałuch (2010)
Annales Polonici Mathematici
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A theorem on the existence of weak solutions of the Cauchy problem for first order functional differential equations defined on the Haar pyramid is proved. The initial problem is transformed into a system of functional integral equations for the unknown function and for its partial derivatives with respect to spatial variables. The method of bicharacteristics and integral inequalities are applied. Differential equations with deviated variables and differential integral equations can...
I. Kubiaczyk, S. Szufla (1982)
Publications de l'Institut Mathématique
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Eduardo Hernández M., Hernán R. Henríquez (2004)
Annales Polonici Mathematici
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By using the theory of strongly continuous cosine families and the properties of completely continuous maps, we study the existence of mild, strong, classical and asymptotically almost periodic solutions for a functional second order abstract Cauchy problem with nonlocal conditions.
Kuo-Wang Chen (1964)
Commentationes Mathematicae Universitatis Carolinae
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Łukasz Dawidowski (2015)
Annales Mathematicae Silesianae
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The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity...