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Quadratic functionals with a variable singular end point. (English) Zbl 0779.49026

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.

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
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