Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem.
Byszewski, Ludwik (1999)
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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Byszewski, Ludwik, Akca, Haydar (1997)
Journal of Applied Mathematics and Stochastic Analysis
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Byszewski, L. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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P. Besala (1983)
Annales Polonici Mathematici
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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.
Kołodziej, Katarzyna (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Aizicovici, Sergiu, Gao, Yun (1997)
Journal of Applied Mathematics and Stochastic Analysis
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Marija Skendžić (1970)
Publications de l'Institut Mathématique
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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.
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.
W. Tutschke (1986)
Matematički Vesnik
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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.
Jan Persson (1976)
Publications mathématiques et informatique de Rennes
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T. Śliwa (1988)
Applicationes Mathematicae
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Oleg Zubelevich (2004)
Open Mathematics
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We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.
Filali, M., Moussi, M. (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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J. Ligęza (1975)
Colloquium Mathematicae
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