INTEGRO-DIFFERENTIAL EVOLUTION NONLOCAL PROBLEM
FOR THE FIRST ORDER EQUATION (II)
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INTEGRO-DIFFERENTIAL EVOLUTION NONLOCAL PROBLEM
FOR THE FIRST ORDER EQUATION (II)
Publication date: 09.02.2015
Technical Transactions, 2014, Nauki Podstawowe Issue 2 NP (16) 2014, pp. 11 - 14
https://doi.org/10.4467/2353737XCT.14.295.3383Authors
INTEGRO-DIFFERENTIAL EVOLUTION NONLOCAL PROBLEM
FOR THE FIRST ORDER EQUATION (II)
The aim of this paper is to give two theorems on the existence and uniqueness of mild and classical solutions of a nonlocal semilinear integro-differential evolution Cauchy problem for the first order equation. The method of semigroups, the Banach fixed-point theorem and the Bochenek theorem are applied to prove the existence and uniqueness of the solutions of the considered problem.
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.
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., Winiarska T., Integrodifferential evolution nonlocal problem for the first order equations, Technical Transactions, Fundamental Sciences, 1 – NP/2011, 15—21.
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Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer–Verlag, New York, Berlin, Heidelberg, Tokyo 1983.
Tidke H. L., Existence of solutions of nonlinear mixed integrodifferential equations of Sobolev type, Nonlinear Functional Analysis and Applications, 14.4, 2009, 605—618.
Information: Technical Transactions, 2014, Nauki Podstawowe Issue 2 NP (16) 2014, pp. 11 - 14
Article type: Original article
Titles:
INTEGRO-DIFFERENTIAL EVOLUTION NONLOCAL PROBLEM
FOR THE FIRST ORDER EQUATION (II)
INTEGRO-DIFFERENTIAL EVOLUTION NONLOCAL PROBLEM
FOR THE FIRST ORDER EQUATION (II)
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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