ON EIGENCURVES OF ELLIPTIC BOUNDARY-VALUE-PROBLEMS

Let T be a selfadjoint uniformly elliptic partial differential operator on a bounded domain in R(n), and let S be a (possibly indefinite) L infinity multiplication operator. Estimates of the form sigma-lambda + omicron-(lambda) and sigma-lambda + beta + omicron-(1) are sought for the eigenvalues mu-(lambda) of lambda-S - T as lambda --> +/- infinity. A necessar and sufficient condition is also obtained for existence of linear eigencurves, i.e. mu-(lambda) = sigma-lambda + beta.