A fixed point theorem for affine mappings and its application to elasticity theory

Oleg Zubelevich

Open Mathematics (2010)

  • Volume: 8, Issue: 6, page 1104-1108
  • ISSN: 2391-5455

Abstract

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In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.

How to cite

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Oleg Zubelevich. "A fixed point theorem for affine mappings and its application to elasticity theory." Open Mathematics 8.6 (2010): 1104-1108. <http://eudml.org/doc/269187>.

@article{OlegZubelevich2010,
abstract = {In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.},
author = {Oleg Zubelevich},
journal = {Open Mathematics},
keywords = {Fixed point theory; Periodic solution; Linear elasticity; Lamé equations; fixed point theory; periodic solution; linear elasticity},
language = {eng},
number = {6},
pages = {1104-1108},
title = {A fixed point theorem for affine mappings and its application to elasticity theory},
url = {http://eudml.org/doc/269187},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Oleg Zubelevich
TI - A fixed point theorem for affine mappings and its application to elasticity theory
JO - Open Mathematics
PY - 2010
VL - 8
IS - 6
SP - 1104
EP - 1108
AB - In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.
LA - eng
KW - Fixed point theory; Periodic solution; Linear elasticity; Lamé equations; fixed point theory; periodic solution; linear elasticity
UR - http://eudml.org/doc/269187
ER -

References

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  8. [8] Murakami S., Naito T., Minh N.V., Massera’s theorem for almost periodicity of solutions of functional differential equations, J. Math. Soc. Japan (in press) Zbl1070.34093
  9. [9] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., 44, Springer, Berlin, 1983 Zbl0516.47023
  10. [10] Shin J.S., Naito T., Semi-Fredholm operators and periodic solutions for linear functional differential equations, J. Differential Equations, 1999, 153(2), 407–441 http://dx.doi.org/10.1006/jdeq.1998.3547 
  11. [11] Yoshizawa T., Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Appl. Math. Sci., 14, Springer, Berlin-Heidelberg-New York, 1975 
  12. [12] Yosida K., Functional Analysis, Springer, Berlin-Göttingen-Heidelberg, 1965 

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