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Keywords:
quadratic functional; singular quadratic functional; Euler-Lagrange equation; conjugate point; coupled point; singularity condition
quadratic functional; singular quadratic functional; Euler-Lagrange equation; conjugate point; coupled point; singularity condition
Summary:
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.
References:
[1] Morse M., Leighton W.: Singular quadratic functionals. Trans. Amer. Math. Soc. 40 (1936), 252-286. MR 1501873 | Zbl 0015.02701
[2] Leighton W.: Principal quadratic functionals. Trans. Amer. Math. Soc. 67 (1949), 253-274. MR 0034535 | Zbl 0041.22404
[3] Leighton W., Martin A.D.: Quadratic functionals with a singular end point. Trans. Amer. Math. Soc. 78 (1955), 98-128. MR 0066570 | Zbl 0064.35401
[4] Reid W.T.: Sturmian theory for ordinary differential equations. Springer-Verlag 1980. MR 0606199 | Zbl 0459.34001
[5] Zeidan V., Zezza P.: Coupled points in the calculus of variations and applications to periodic problems. Trans. Amer. Math. Soc. 315 (1989), 323-335. MR 0961599 | Zbl 0677.49020
[6] Zeidan V., Zezza P.: Variable end points in the calculus of variations: Coupled points. in ``Analysis and Optimization of Systems'', A. Bensoussan, J.L. Lions eds., Lectures Notes in Control and Information Sci. 111, Springer-Verlag, Heidelberg, 1988. MR 0956284
[7] Zezza P.: The Jacobi condition for elliptic forms in Hilbert spaces. JOTA 76 (1993). MR 1203907
[8] Zezza P., Došlá Z.: Coupled points in the calculus of variations and optimal control theory via the quadratic form theory. preprint.
[9] Coppel W.A.: Disconjugacy. Lecture Notes in Math. 220, Springer-Verlag, Berlin-Heidelberg, 1971. MR 0460785 | Zbl 0224.34003
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