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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The two-parameter Sturm-Liouville problem for ordinary differential equations. II
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by B. D. Sleeman PDF
Proc. Amer. Math. Soc. 34 (1972), 165-170 Request permission

Abstract:

The object of this note is to discuss the existence under fairly general conditions of solutions of the two-parameter eigenvalue problem defined by the pair of differential equations \[ {d^2}{y_i}/dx_i^2 + \{ {q_i}({x_i};\lambda ,\mu ) + {r_i}({x_i})\} {y_i} = 0,\quad i = 1,2,{x_i} \in [0,1],\] and associated two-point Sturm-Liouville end conditions.
References
  • B. D. Sleeman, The two parameter Sturm-Liouville problem for ordinary differential equations, Proc. Roy. Soc. Edinburgh Sect. A 69 (1970/71), 139–148. MR 291543
  • M. Faierman, The completeness and expansion theorems associated with the multi-parameter eigenvalue problem in ordinary differential equations, J. Differential Equations 5 (1969), 197–213. MR 232991, DOI 10.1016/0022-0396(69)90112-0
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 165-170
  • MSC: Primary 34B25
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0291544-7
  • MathSciNet review: 0291544