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

Resumo

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.