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We study the influence of the rattling phonons on superconductivity in$\beta$-pyrochlore KOs$_{2}$O$_{6}$ compound based on the strong-couplingEliashberg approach. In particular, analyzing the specific heat data we findthat the rattling phonon frequency changes discontinuously at the criticaltemperature of the first order phase transition. Solving the strong-couplingEliashberg equations with temperature dependent $\alpha^{2}F(\omega)$, weinvestigate the consequence of this first order phase transition for theanomalous temperature dependence of the superconducting gap. We discuss ourresults in context of the recent experimental data.

Superconductivity in $\beta$-pyrochlore superconductor KOs$_{2}$O$_{6}$: treatment within strong-coupling Eliashberg theory