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Kopáčková, Marie
On periodic solutions of some equations of mathematical physics. (English). Aplikace matematiky, vol. 18 (1973), issue 1, pp. 33-42
MSC: 35B10, 35G30, 35L35, 35L99 | MR 0312044 | Zbl 0249.35057 | DOI: 10.21136/AM.1973.103446
Summary:
Some linear and weakly nonlinear partial differential equations with Dirichlet boundary conditions are treated. The necessary and sufficient conditions for the existence and uniqueness of a periodic solution are given and several examples from classical physics are included.
References:
[1] O. Vejvoda: Periodic solution of a linear and weakly nonlinear wave equation in one dimension. Czech. Mat. Journ. 14 (89), 1964. MR 0174872 | Zbl 0178.45302
[2] M. Sova: Abstract semilinear equations with small nonlinearities. CMUC, no 4, p. 685,1971. MR 0291912 | Zbl 0235.47034
[3] N. Krylová: Periodic solutions of hyperbolic partial differential equation with quadratic dissipative term. Czech. Mat. Journ. 20 (95), 1970. MR 0283358
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