Stuart, C. A.2017-07-102017-07-102017-07-10201710.1016/j.na.2017.04.001https://infoscience.epfl.ch/handle/20.500.14299/138917WOS:000404198900005We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The derivative is required to be Gateaux differentiable at u(0), but positive definiteness of f ''(u(0)) does not even ensure that f has a local minimum at u(0) when f' is not Frechet differentiable at u(0). This issue is also discussed in the context of the energy functional for a parameter dependent nonlinear eigenvalue problem and then for a particular case involving a degenerate elliptic Dirichlet problem on a bounded domain in R-N. (C) 2017 Elsevier Ltd. All rights reserved.Local minimumExtremumNonlinear eigenvalue problemtext::journal::journal article::research article