  We consider the stability of an ultracold trapped Bose-Einstein condensate
near a Feshbach resonance. Using a modified Gross-Pitaevskii equation that
includes higher-order terms and a multi-channel model of Feshbach resonances,
we find regions where stability can be enhanced or suppressed around
experimentally measured resonances. We suggest a number of ways to probe the
stability diagram. Using scattering length zero-crossings huge deviations are
founds for the critical particle number. Effects are enhanced for narrow
resonances or tighter traps. Macroscopic tunneling of the condensate is another
possible probe for higher-order interactions, however, to see this requires
very narrow resonances or very small particle numbers.
