EIGENVALUE AND EIGENFUNCTION ASYMPTOTICS FOR REGULAR STURM-LIOUVILLE PROBLEMS

In this paper, we obtain asymptotic formulas for eigenvalues, eigenfunctions, and the reciprocals of the eigenfunction norms for eigenvalue problems associated with the general Sturm-Liouville equation (pu')' + (lambda r - q) u = 0 having regular endpoints. The method is based on a conversion to Liouville Normal Form and an iterative procedure of solving the associated Volterra integral equation, producing an asymptotic expansion of the solution in higher powers of 1/lambda(1/2) as lambda --> infinity. (C) 1994 Academic Press, Inc.