Displaying similar documents to “On second–order Taylor expansion of critical values”

Clarke critical values of subanalytic Lipschitz continuous functions

Jérôme Bolte, Aris Daniilidis, Adrian Lewis, Masahiro Shiota (2005)

Annales Polonici Mathematici

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The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawłucki's extension of the Puiseux lemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

A critical point result for non-differentiable indefinite functionals

Salvatore A. Marano, Dumitru Motreanu (2004)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, two deformation lemmas concerning a family of indefinite, non necessarily continuously differentiable functionals are proved. A critical point theorem, which extends the classical result of Benci-Rabinowitz [14, Theorem 5.29] to the above-mentioned setting, is then deduced.

Discontinuous quasilinear elliptic problems at resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1998)

Colloquium Mathematicae

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In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.

Finding linking sets.

Schechter, Martin, Tintarev, Kyril (2006)

International Journal of Mathematics and Mathematical Sciences

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Perturbations of Critical Values in Nonsmooth Critical Point Theory

Degiovanni, M., Lancelotti, S. (1996)

Serdica Mathematical Journal

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* Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993). ** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993). The perturbation of critical values for continuous functionals is studied. An application to eigenvalue problems for variational inequalities is provided.

Lipschitz modulus in convex semi-infinite optimization via d.c. functions

María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem’s data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably...

A min-max theorem for multiple integrals of the Calculus of Variations and applications

David Arcoya, Lucio Boccardo (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper we deal with the existence of critical points for functionals defined on the Sobolev space W 0 1 , 2 ⁢ Ω by J ⁢ v = ∫ Ω I ⁢ x , v , D ⁢ v ⁢ d ⁢ x , v ∈ W 0 1 , 2 ⁢ Ω , where Ω is a bounded, open subset of R N . Since the differentiability can fail even for very simple examples of functionals defined through multiple integrals of Calculus of Variations, we give a suitable version of the Ambrosetti-Rabinowitz Mountain Pass Theorem, which enables us to the study of critical points for functionals which are not differentiable in all directions....