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Vejvoda, Otto ; Krejčí, Pavel
A note to a bifurcation result of H. Kielhöfer for the wave equation. (English). Mathematica Bohemica, vol. 116 (1991), issue 3, pp. 245-247
MSC: 11J25, 35B10, 35B32, 35L70 | MR 1126446 | Zbl 0773.35008 | DOI: 10.21136/MB.1991.126179
Keywords:
Diophantine approximations; wave equation; periodic solution; bifurcation
Summary:
A modification of a classical number-theorem on Diophantine approximations is used for generalizing H. kielhöfer's result on bifurcations of nontrivial periodic solutions to nonlinear wave equations.
References:
[1] H. Kielhöfer: Bifurcation of periodic solution for a semilinear wave equation. J. Math. Anal. Appl. 68 (1979), 408-420. DOI 10.1016/0022-247X(79)90125-2
[2] H. Kielhöfer P. Kötzner: Stable periods of a semilinear wave equation and bifurcation of periodic solutions. j. Appl. Math. Phys. (ZAMP) 38 (1987), 204-212. DOI 10.1007/BF00945406
[3] J. W. S. Cassels: An introduction to Diophantine approximation. Cambridge University Press no. 45, Cambridge, 1957. MR 0087708 | Zbl 0077.04801
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