Došlá, Zuzana; Zezza, Pier Luigi Quadratic functionals with a variable singular end point. (English) Zbl 0779.49026 Commentat. Math. Univ. Carol. 33, No. 3, 411-425 (1992). Summary: 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 non-negativity of these functionals. Cited in 1 ReviewCited in 1 Document MSC: 49K15 Optimality conditions for problems involving ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations Keywords:singular quadratic functional; Euler-Lagrange equation; conjugate point; coupled point; necessary and sufficient conditions PDF BibTeX XML Cite \textit{Z. Došlá} and \textit{P. L. Zezza}, Commentat. Math. Univ. Carol. 33, No. 3, 411--425 (1992; Zbl 0779.49026) Full Text: EuDML OpenURL