Unstable simple modes for a class of Kirchhoff equations
نویسندگان
چکیده
It is well known that Kirchhoff equations admit infinitely many simple modes, i. e. time periodic solutions with only one Fourier component in the space variables. We prove that, for some choices of the nonlinearity, these simple modes are unstable provided that their energy is large enough. This result, stated in an abstract Hilbert space setting, and proved by reducing to a system of two second order ODEs, applies to PDEs of Kirchhoff type on bounded domains of
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