Detectability of critical points of smooth functionals from their finite-dimensional approximations

作者：Sani F; Villarini M^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(9): 3140-3150.

DOI：10.1016/j.na.2010.06.086

• Rayleigh-Ritz-Galerkin approximations
• Approximations of critical points
• Hamiltonian systems

Given a critical point of a C(2)-functional on a separable Hilbert space, we obtain sufficient conditions for it to be detectable (i.e. 'visible') from finite-dimensional Rayleigh-Ritz- Galerkin (RRG) approximations. While examples show that even nondegenerate critical points are, without any further restriction, not visible, we single out relevant classes of smooth functionals, e.g. the Hamiltonian action on the loop space or the functionals associated with boundary value problems for somes emilinear elliptic equations, such that their nondegenerate critical points are visible from their RRG approximations.

• 出版日期2010-11-1