  We present a coupled system of integral equations for the pi pi --> Nbar N
and Kbar K --> Nbar N S-waves derived from Roy-Steiner equations for
pion-nucleon scattering. We discuss the solution of the corresponding
two-channel Muskhelishvili-Omnes problem and apply the results to a dispersive
analysis of the scalar form factor of the nucleon fully including Kbar K
intermediate states. In particular, we determine the corrections Delta_sigma
and Delta_D, which are needed for the extraction of the pion-nucleon sigma term
from pi N scattering, and show that the difference Delta_D - Delta_sigma=(-1.8
+/- 0.2) MeV is insensitive to the input pi N parameters.
