Periodic solutions of a linear and weakly nonlinear wave equation in one dimension, I
In the paper the conditions for the existence of a -periodic solution in of the system , are investigated provided that is sufficiently smooth and -periodic in .
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.
One investigates the existence of an -periodic solution of the problem , provided the functions are sufficiently smooth and -periodic in . If , natural, such a solution always exists for sufficiently small . On the other hand, if , natural, some additional conditions have to be satisfied.
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