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Atkinson, F.V. and Mingarelli, A.B. (1987) Asymptotics of the Number of Zeros and of the Eigenvalues of General Weighted Sturm-Liouville Problems. Journal fur die Reine und Angewandte Mathematik, 375-376, 380-393.

has been cited by the following article:

• TITLE: Estimating the Lower Bounds on the Eigenvalue of the Smallest Modulus in the Case of Mixed Boundary Conditions

  AUTHORS: Boas Chisha, Mervis Kikonko

  KEYWORDS: Eigenvalue, Eigenfunction, Fredholm Integral Operator, Greens Function, Integral Equations, Non-Definite, Right-Definite, Left-Definite, Mixed Boundary Conditions

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.6, June 24, 2026

  ABSTRACT: We derive a lower bound on the eigenvalue of the smallest modulus associated with a mixed boundary condition problem in the general case of a regular Sturm-Liouville problem. Using the Fredholm integral operator and estimates on its norm, we derive bounds for the eigenvalue of the smallest modulus under the assumption that the coefficient function q( x ) and the weight function r( x ) exhibit no sign restrictions. The results contribute to a broader understanding of eigenvalue problems with mixed boundary conditions in the general case of the regular Sturm-Liouville problems. We also recommend similar studies in higher order Sturm-Liouville problems.