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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.14.295.3383

Authors

,
Ludwik Byszewski
Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology
https://orcid.org/0000-0001-7227-8990 Orcid
All publications →
Teresa Winiarska
Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology
All publications →

Titles

INTEGRO-DIFFERENTIAL EVOLUTION NONLOCAL PROBLEM
FOR THE FIRST ORDER EQUATION (II)

Abstract

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.

References

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.

Information

Information: Technical Transactions, 2014, Nauki Podstawowe Issue 2 NP (16) 2014, pp. 11 - 14

Article type: Original article

Titles:

Polish:

INTEGRO-DIFFERENTIAL EVOLUTION NONLOCAL PROBLEM
FOR THE FIRST ORDER EQUATION (II)

English:

INTEGRO-DIFFERENTIAL EVOLUTION NONLOCAL PROBLEM
FOR THE FIRST ORDER EQUATION (II)

Authors

https://orcid.org/0000-0001-7227-8990

Ludwik Byszewski
Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology
https://orcid.org/0000-0001-7227-8990 Orcid
All publications →

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

Percentage share of authors:

Ludwik Byszewski (Author) - 50%
Teresa Winiarska (Author) - 50%

Article corrections:

-

Publication languages:

English