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Necessary condition for an Euler-Lagrange equation on time scales. (English) Zbl 1448.81304

Summary: We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
70H03 Lagrange’s equations
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