Geodesic
Quadratic functionals with a variable singular end point
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 411-425.

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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.
Classification : 34A10, 34A12, 34C10, 49B10, 49K05, 49K15
Keywords: quadratic functional; singular quadratic functional; Euler-Lagrange equation; conjugate point; coupled point; singularity condition 
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     title = {Quadratic functionals with a variable singular end point},
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Došlá, Zuzana; Zezza, PierLuigi. Quadratic functionals with a variable singular end point. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 411-425. http://geodesic.mathdoc.fr/item/CMUC_1992__33_3_a4/