Towards a solution of the inverse problem of the calculus of variations for scalar ordinary differential equations1
نویسنده
چکیده
We state a combinatorial conjecture, which, if true, yields a simple solution to the multiplier version of the inverse problem of the calculus of variations. With the help of a computer, we verified our conjecture for 3 ≤ n ≤ 100, and thus found necessary and sufficient conditions for a 2nth-order scalar ordinary differential equation ∂2nu/∂x2n = f (x, u, ∂u/∂x, . . . , ∂2n−1u/∂x2n−1), 3 ≤ n ≤ 100, to admit a variational multiplier.
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