Direct methods for the solution of singular integral equations with finite number of different zeros in pairwise.

Al-Faqih, Feras M.

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In this paper we introduce the definition of coupled point with respect to a (scalar) quadratic functional on a noncompact interval. In terms of coupled points we prove necessary (and sufficient) conditions for the nonnegativity of these functionals.

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Commentationes Mathematicae Universitatis Carolinae

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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 and . The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions.

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