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An abstract nonlocal functional-differential second order evolution Cauchy problem

Publication date: 27.04.2018

Technical Transactions, 2018, Volume 4 Year 2018 (115), pp. 139-147

https://doi.org/10.4467/2353737XCT.18.062.8374

Authors

,
Adam Bednarz
Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology
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Ludwik Byszewski
Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology
https://orcid.org/0000-0001-7227-8990 Orcid
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An abstract nonlocal functional-differential second order evolution Cauchy problem

Abstract

The aim of the paper is to prove two theorems on the existence and uniqueness of mild and classical solutions of a semilinear functional-differential evolution second order equation together with nonlocal initial conditions. The theory of strongly continuous cosine families of linear operators in a Banach space is applied. The paper is based on publications [1–12] and is a generalization of paper [7].

References

[1] 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.
[2] Bednarz A., Byszewski L., On abstract nonlocal Cauchy problem, Technical Transactions, 1-NP/2013, 11–17.
[3] Bochenek J., An abstract nonlinear second order differential equation, Ann. Polon. Math. 54.2, 1991, 155–166.
[4] Bochenek J., Cosine operator functions and condition (F), Selected Problems of Mathematics, Cracow University of Technology Monographs, Anniversary Issue 6, 1995, 13–24.
[5] Bochenek J., Winiarska T., Second order evolution equations with parameter, Ann. Polon. Math. 59.1, 1994, 41–52.
[6] Byszewski L., On some application of the Bochenek theorem, Univ. Iagel. Acta. Math. 45, 2007, 147–153.
[7] Byszewski L., An abstract nonlocal functional-differential second order evolution problem, Technical Transactions 1/2017, 147–154.
[8] Byszewski L., Winiarska T., An abstract nonlocal second order evolution problem, Opuscula Mathematica 32.1, 2012, 75–82.
[9] Cholewa J.W., Dłotko T., Global Attractors in Abstract Parabolic Problems, London Mathematical Society Lecture Notes, Series 278, Cambridge University Press, Cambridge 2000.
[10] Fattorini H. O., Ordinary differential equation in linear topological spaces, J. Differential Equations 5, 1968, 72–105.
[11] Nagy B., Cosine operator functions and the abstract Cauchy problem, Periodica Math. Hungary 7, 1976, 213–217.
[12] Travis C.C., Webb G.F., Cosine family and abstract nonlinear second order differential equations, Acta Math. Hungar. 32, 1978, 75–96.
 

Information

Information: Technical Transactions, 2018, Volume 4 Year 2018 (115), pp. 139-147

Article type: Original article

Titles:

Polish:

An abstract nonlocal functional-differential second order evolution Cauchy problem

English:

An abstract nonlocal functional-differential second order evolution Cauchy problem

Authors

Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology

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
Contact with author
All publications →

Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology

Published at: 27.04.2018

Article status: Open

Licence: None

Percentage share of authors:

Adam Bednarz (Author) - 50%
Ludwik Byszewski (Author) - 50%

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