Abstract
We consider the boundary-value problem u tt + ɛu t + (1 + ɛαcos2τ)sin u =ɛσ2 u xx, u x|x=0=ux|x=π=0, where 0<ɛ≪1, τ=(1+ɛδ)t, α,σ> 0, and the sign of δ is arbitrary. It is proved that for an appropriate choice of the external parameters α and δ and for sufficiently small σ the number of exponentially stable solutions 2π-periodic in τ can be made equal to an arbitrary predefined number.
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Kolesov, A.Y., Rozov, N.K. The Parametric Buffer Phenomenon for a Singularly Perturbed Telegraph Equation with a Pendulum Nonlinearity. Mathematical Notes 69, 790–798 (2001). https://doi.org/10.1023/A:1010230431593
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DOI: https://doi.org/10.1023/A:1010230431593