Criteria for the existence of a potential well

We 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.


Published in:
Nonlinear Analysis-Theory Methods & Applications, 158, 83-108
Year:
2017
Publisher:
Oxford, Pergamon-Elsevier Science Ltd
ISSN:
0362-546X
Keywords:
Laboratories:




 Record created 2017-07-10, last modified 2018-12-03


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