Existence Conditions of Negative Eigenvalues in the Regular Sturm–Liouville Boundary Value Problem and Explicit Expressions for Their Number
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For the regular Sturm–Liouville boundary value problem with general nonseparated self-adjoint 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.
Keywords:Sturm–Liouville equation boundary value problem eigenvalue
I am grateful to N.B. Konyukhova for discussions of this paper and to the reviewer of its first version for valuable remarks that enabled me to improve the presentation.
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