volume 15, issue 9, P1181-1182 1985
DOI: 10.1070/qe1985v015n09abeh007655
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Abstract: In this paper, we consider the higher dimensional nonlinear beam equations u tt + 2 u + σ u + f (u) = 0, with periodic boundary conditions, where the nonlinearity f (u) is a realanalytic function near u = 0 with f (0) = f (0) = 0 and σ is a real parameter in an interval I ≡ [σ 1 , σ 2 ]. It is proved that for 'most' positive parameters σ lying in the finite interval I, the above equations admit a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to a Cantor family of finite dim…

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