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Titlebook: Differential Equations, Chaos and Variational Problems; Vasile Staicu Conference proceedings 2008 Birkhäuser Basel 2008 Boundary value pro

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On the Euler-Lagrange Equation for a Variational Problem, with non empty interior. By means of a disintegration theorem, we next show that the Euler-Lagrange equation can be reduced to an ODE along characteristics, and we deduce that the solution to Euler-Lagrange is different from 0 a.e. and satisfies a uniqueness property. Using these results, we prove
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Necessary Conditions in Optimal Control and in the Calculus of Variations,ented and refined over the last thirty years in connection with the nonsmooth analysis approach. Specifically, we present a proof of Theorem 2.1 below, which asserts all the first-order necessary conditions for the basic problem in the calculus of variations, and a proof of Theorem 3.1, which is the
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On Bounded Trajectories for Some Non-Autonomous Systems,ion and .(±1) = 0. In addition, we consider the existence of a solution to the boundary value problem in the half line . where . ≥ 0 and . is a .., non-negative function, such that . (0) = . (1) = 0. If . = 0 and . and . are even, it turns out that these solutions yield heteroclinics for a special c
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