We study a problem from nonlinear optics that leads to an integro-different
ial equation which can be written as the abstract bifurcation problem Au =
lambda Lu + del phi (u). For such a type of equation, a general theorem on
the bifurcation of solutions from the essential spectrum is proved. The hyp
othesis that phi is non-negative (as is usually assumed) could be omitted a
nd replaced by other conditions that allow us to use the results for the pa
rticular example. We also indicate applications to semilinear elliptic equa
tions.