Dynamic von Kármań equations involving nonlinear damping: Time- periodic solutions. (English) Zbl 0676.73026

Time-periodic solutions to dynamic von Kármán equations are investigated. For a damped system the author shows the existence of at least one solution to the problem. The Faedo-Galerkin method is used together with some basic ideas concerning monotone operators on Orlicz spaces.
Reviewer: K.Brod


74K20 Plates
74H45 Vibrations in dynamical problems in solid mechanics
35B10 Periodic solutions to PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
Full Text: DOI EuDML


[1] H. Gajewski K. Gröger K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag Berlin 1974. · Zbl 0289.47029
[2] A. Haraux: Dissipativity in the sense of Levinson for a class of second-order nonlinear evolution equations. Nonlinear Anal. 6 (1982), pp. 1207-1220. · Zbl 0505.35012 · doi:10.1016/0362-546X(82)90031-1
[3] A. Kufner O. John S. Fučík: Function spaces. Academia Praha 1977.
[4] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris 1969. · Zbl 0189.40603
[5] J. L. Lions, E. Magenes: Problèmes aux limites non homogènes et applications 1. Dunod, Paris 1968. · Zbl 0165.10801
[6] N. F. Morozov: Selected two-dimensional problems of the elasticity theory. (Russian.) Leningrad 1978.
[7] M. Nakao: Periodic solution and decay for some nonlinear wave equations with sublinear dissipative terms. Nonlinear Anal. 10 (1986), pp. 587 - 602. · Zbl 0601.35075 · doi:10.1016/0362-546X(86)90144-6
[8] G. Prodi: Soluzioni periodiche di equazioni a derivative parziali di tipo iperbolico non lineari. Ann. Mat. Pura Appl. 42 (1956), pp. 25 - 49. · Zbl 0072.10101 · doi:10.1007/BF02411872
[9] G. Prouse: Soluzioni periodiche dell’equazione deile onde non omogenea con termine dissipativo quadratico. Ricerche Mat. 13 (1964), pp. 261 - 280. · Zbl 0141.28804
[10] P. H. Rabinowitz: Free vibrations for a semi-linear wave equation. Comm. Pure Appl. Math. 31 (1978), pp. 31-68. · Zbl 0341.35051 · doi:10.1002/cpa.3160310103
[11] A. Stahel: A remark on the equation of a vibrating plate. Proc. Royal Soc. Edinburgh 106 A (1987), pp. 307-314. · Zbl 0625.73064 · doi:10.1017/S0308210500018436
[12] O. Vejvoda, al.: Partial differential equations: Time-periodic solutions. Martinus Nijhoff, The Hague 1982. · Zbl 0501.35001
[13] W. von Wahl: On nonlinear evolution equations in a Banach space and nonlinear vibrations of the clamped plate. Bayreuther Mathematische Schriften, 7 (1981), pp. 1 - 93.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.