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Proceedings of the American Mathematical Society

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The two-parameter Sturm-Liouville problem for ordinary differential equations. II


Author: B. D. Sleeman
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
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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

$\displaystyle {d^2}{y_i}/dx_i^2 + \{ {q_i}({x_i};\lambda ,\mu ) + {r_i}({x_i})\} {y_i} = 0,\quad i = 1,2,{x_i} \in [0,1],$

and associated two-point Sturm-Liouville end conditions.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291544-7
Keywords: Two-parameter Sturm-Liouville problem, existence, number of zeros of solution
Article copyright: © Copyright 1972 American Mathematical Society