ON NONLOCAL EVOLUTION FUNCTIONAL-DIFFERENTIAL PROBLEM
IN A BANACH SPACE
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ON NONLOCAL EVOLUTION FUNCTIONAL-DIFFERENTIAL PROBLEM
IN A BANACH SPACE
Publication date: 09.02.2015
Technical Transactions, 2014, Nauki Podstawowe Issue 2 NP (16) 2014, pp. 1 - 1
https://doi.org/10.4467/2353737XCT.14.296.3384Authors
ON NONLOCAL EVOLUTION FUNCTIONAL-DIFFERENTIAL PROBLEM
IN A BANACH SPACE
The aim of this paper is to prove two theorems on the existence and uniqueness of mild and classical solutions of a nonlocal semilinear functional-differential evolution Cauchy problem in a Banach space. The method of semigroups, the Banach fixed-point theorem and the Bochenek theorem (see [3]) about the existence and uniqueness of the classical solution of the first order differential evolution problem in a not necessarily reflexive Banach space are used to prove the existence and uniqueness of the solutions of the considered problem. The results are based on publications [1 — 8].
Balachandran K., Ilamaran S., Existence and uniqueness of mild and strong solutions of a semilinear evolution equation with nonlocal conditions, Indian J. Pure Appl. Math., 25.4, 1994, 411—418.
Balasubramaniam, P. Chandrasekaran, M. Existence of solutions of nonlinear integrodifferential equation with nonlocal boundary conditions in Banach space, Atti Sem. Mat. Fis. Univ. Modena, 46, 1998, 1—13.
Bochenek J., The existence of a solution of a semilinear first–order differential equation in a Banach space, Univ. Iag. Acta Math., 31 1994, 61—68.
Byszewski L., Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162.2 1991, 494—505.
Kato T., Perturbation Theory for Linear Operators, Springer-Verlag, New York, Berlin, Heidelberg 1966.
Kołodziej K., Existence and uniqueness of solutions of a semilinear functionaldifferential evolution nonlocal Cauchy problem, JAMSA, 13.2 2000, 171–179.
Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer–Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
Winiarska T., Differential Equations with Parameters, Monograph 68, Cracow University of Technology 1988.
Information: Technical Transactions, 2014, Nauki Podstawowe Issue 2 NP (16) 2014, pp. 1 - 1
Article type: Original article
Titles:
ON NONLOCAL EVOLUTION FUNCTIONAL-DIFFERENTIAL PROBLEM
IN A BANACH SPACE
ON NONLOCAL EVOLUTION FUNCTIONAL-DIFFERENTIAL PROBLEM
IN A BANACH SPACE
Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology
Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology
Published at: 09.02.2015
Article status: Open
Licence: None
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