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Titlebook: Calculus of Variations I; Mariano Giaquinta,Stefan Hildebrandt Book 2004 Springer-Verlag Berlin Heidelberg 2004 Calculus of Variations.Con

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Calculus of Variations I978-3-662-03278-7Series ISSN 0072-7830 Series E-ISSN 2196-9701
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Fundamentals of Dynamic Systems,oint . is sufficient to guarantee that . is a relative minimizer. In other words, the assumption ...(.) > 0 for the stationary point . implies that . for all . in a sufficiently small neighbourhood of . in ℝ..
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Fundamentals of Dynamic Systems,oint . is sufficient to guarantee that . is a relative minimizer. In other words, the assumption ...(.) > 0 for the stationary point . implies that . for all . in a sufficiently small neighbourhood of . in ℝ..
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Huajin Tang,Kay Chen Tan,Zhang Yigiven extremal . of a variational integral . is, in fact, a .. This will be achieved by a method the elements of which were developed by Weierstrass. One of its basic ideas is to consider a whole bundle of extremals instead of a single one, just as one investigates in optics . instead of isolated si
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https://doi.org/10.1007/978-3-662-03278-7Calculus of Variations; Convexity; Gaussian curvature; Hamiltonian Formalism; Lagrangian Formalism; Mean
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978-3-642-08074-6Springer-Verlag Berlin Heidelberg 2004
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Baochang Zhang,Tiancheng Wang,David DoermannIn the first two chapters we have investigated the rate of change of variational integrals ℱ with respect to variations of the dependent variables. In particular, we have derived the necessary conditions . and .for extremizers u of ℱ, and suitable modifications of these conditions were shown to hold for constrained extremizers.
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https://doi.org/10.1007/978-1-4471-3087-1If .(u) is a real valued function of a real variable which is of class .. on ℝ, then, besides .′(u.) = 0, also the condition .″(u.) ≥ 0 is necessary for .. being a local minimizer of .. Moreover, the conditions . are sufficient for .. furnishing a local minimum.
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