A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam

By B. Breuer, J. Horák, P. J. McKenna, Michael Plum. 2006

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Computation of maximal local (un)stable manifold patches by the parameterization method (2015, unknown): “see [59, 60]) ∂2u ∂t2 = − 4u ∂x4 − (e − 1) .”
Verification methods: rigorous results using floating-point arithmetic (2010, result): “We wish to remark that, two years after publication of this result, Dancer and Yan (2005) gave a more general analytical proof (which we believe was stimulated by Breuer et al. (2003)); they even proved that the number of solutions of problem (16.”