Asymptotic Formulae for the Eigenvalues of a Two-parameter Ordinary Differential Equation of the Second Order(')
نویسنده
چکیده
We consider a two-point boundary value problem associated with an ordinary differential equation defined over the unit interval and containing the two parameters A and p. If for each real p. we denote the zzith eigenvalue of our system by Am(/j.), then it is known that Am(/j.) is real analytic in — co co, and indeed obtain such a development to an accuracy determined by the coefficients of our differential equation. With suitable conditions on the coefficients of our differential equation, the asymptotic formula for ¡\m(p) may be further developed using the methods of this paper. These results may be modified so as to apply to A„,(/j.) as p.-*— co if the coefficients of our differential equation are also suitably modified.
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