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)
Data publikacji: 09.02.2015
Czasopismo Techniczne, 2014, Nauki Podstawowe Zeszyt 2 NP (16) 2014, s. 11 - 14
https://doi.org/10.4467/2353737XCT.14.295.3383Autorzy
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.
Kato T., Perturbation Theory for Linear Operators, Springer - Verlag, New York, Berlin, Heidelberg 1966.
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.
Informacje: Czasopismo Techniczne, 2014, Nauki Podstawowe Zeszyt 2 NP (16) 2014, s. 11 - 14
Typ artykułu: Oryginalny artykuł naukowy
Tytuły:
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
Publikacja: 09.02.2015
Status artykułu: Otwarte
Licencja: Żadna
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