Higher order asymptotic distribution of the eigenvalues of nondefinite Sturm--Liouville problems with one turning point

  • Authors:

  • A. Jodayree Akbarfam;Angelo B. Mingarelli

  • Affiliations:

  • Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran;School of Mathematics and Statistics, Carleton University, Ottawa, Ont., Canada K1S 5B6

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2002

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Abstract

In this paper we derive the higher order asymptotic distribution of the positive eigenvalues associated with a linear real second order equation y'' + (λxα - q(x))y = 0, of Sturm-Liouville type on [a,b] with Dirichlet boundary condition (i.e., y(a)=y(b)=0), where -∞ a b q is a real-valued sign-indefinite member of C1 [a, b], λ is a real parameter and α - 1 is chosen so that the boundary problem is non-definite.