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Regular version of the site

Article

Existence Conditions of Negative Eigenvalues in the Regular Sturm–Liouville Boundary Value Problem and Explicit Expressions for Their Number

Computational Mathematics and Mathematical Physics. 2018. Vol. 58. No. 12. P. 1937-1947.

For the regular Sturm–Liouville boundary value problem with general nonseparated selfadjoint
boundary conditions, conditions for the existence of zero and negative eigenvalues and expressions
for their number are obtained. The conditions are expresses in a closed form, and the coefficient
functions of the original equation appear in these conditions indirectly through a single numerical
characteristic.