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

Abstract-We consider a nonlinear fourth-order ordinary differential equation on the whole real line, which models travelling waves in a nonlinearly supported beam, e.g. in a suspension bridge. Our aim is to prove that this problem has at least 36 solutions, for a fixed chosen value of the wave speed parameter. Our proof makes heavy use of computer assistance: Starting from numerical approximations, we use a fixedpoint argument to prove existence of solutions "close to" the computed approximations. The main subtask to be accomplished in this argument is an examination of the spectra of the operators arising by linearization at the computed approximations