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Keywords:
quadratic functional; singular quadratic functional; periodic and antiperiodic boundary condition; conjugate point; coupled point; singularity condition
quadratic functional; singular quadratic functional; periodic and antiperiodic boundary condition; conjugate point; coupled point; singularity condition
Summary:
Singular quadratic functionals of one dependent variable with nonseparated boundary conditions are investigated. Necessary and sufficient conditions for nonnegativity of these functionals are derived using the concept of {\it coupled point} and {\it singularity condition}. The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions.
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