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2010 | 8 | 6 | 1104-1108
Tytuł artykułu

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

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EN
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.
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Bibliografia
  • [1] Adams R.A., Sobolev Spaces, Pure Appl. Math., 65, Academic Press, New York-San Francisco-London, 1975
  • [2] Chow S.-N., Hale J.K., Strongly limit-compact maps, Funkcial. Ekvac., 1974, 17(1), 31–38
  • [3] Hino Y., Murakami S., Periodic solutions of a linear Volterra system, In: Differential Equations, Proc. EQUADIFF Conf., Xanthi 1987, Lecture Notes Pure Appl. Math., 118, Dekker, New York, 1989, 319–326
  • [4] Lions J.L., Magenes E., Non-Homogeneous Boundary Value Problems and Applications. Vol. I–III, Grundlehren Math. Wiss., 181–183, Springer, Berlin-Heidelberg-New York, 1972–1973
  • [5] Makay G., Periodic solutions of linear differential and integral equations, Differential Integral Equations, 1995, 8(8), 2177–2187
  • [6] Makay G., On some possible extensions of Massera’s theorem, In: Proceedings of the 6th Colloquium on the Qualitative Theory of Differential Equations, August 10–14, 1999, Szeged, Electron. J. Qual. Theory Differ. Equ., 2000, Suppl., No. 16
  • [7] Massera J., The existence of periodic solutions of systems of differential equations, Duke Math. J., 1950, 17(4), 457–475 http://dx.doi.org/10.1215/S0012-7094-50-01741-8
  • [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)
  • [9] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., 44, Springer, Berlin, 1983
  • [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] 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] Yosida K., Functional Analysis, Springer, Berlin-Göttingen-Heidelberg, 1965
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0067-7
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