  We prove small data global existence for a class of semilinear wave equations
satisfying the null condition on extremal Reissner-Nordstrom black hole
backgrounds with nonlinear terms that degenerate at the event horizon. We
impose no symmetry assumptions. The study of such equations is motivated by
their covariance properties under the Couch-Torrence conformal isometry. We
show decay, non-decay and asymptotic blow-up results analogous to those in the
linear case.
