On the inversion of Lagrange-Dirichlet theorem
Vinicio Moauro, P. Negrini · Differential and Integral Equations · 1989
The inversion of the Lagrange-Dirichlet theorem is proved under the hypothesis that the potential function U of the acting force is h-differentiable, h > 3, and the lack of a local maximum of U at the equilibrium position is recognizable by means of the nonvanishing terms with lowest degree in the expansion of U.This result extends a previous one relative to infinitely differentiable potential functions and is obtained by using known results concerning the existence of invariant stable manifolds.