Results 151 to 160 of about 13,629,063 (179)

Nonsmooth critical point theory and applications

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author surveys recent developments in critical point theory for (not necessarily continuous) functions \(f \colon X \to \overline{\mathbb{R}}\) where \(X\) is a metric space. First he discusses the weak slope \(| df| (u) \in [0,\infty)\) which is defined if \(f(u) \in \mathbb{R}\). This concept is well suited for critical point theory provided that
Marco Degiovanni
exaly   +5 more sources

Subdifferential Calculus and Nonsmooth Critical Point Theory

SIAM Journal on Optimization, 2000
Summary: A general critical point theory for continuous functions defined on metric spaces has been recently developed. A new subdifferential, related to that theory, is introduced. In particular, results on the subdifferential of a sum are proved. An example of application to PDEs is sketched.
Campa, Ines, Degiovanni, Marco
exaly   +6 more sources

A critical point theory for nonsmooth functional

Annali di Matematica Pura ed Applicata, 1994
In this paper a suitable definition of ``norm of differential'' and the notion of critical points are introduced for continuous functionals on metric spaces. By means of this new definition, the classical results of Lyusternik-Schnirelmann on critical point theory for smooth functionals on manifolds are extended to continuous functionals on complete ...
Degiovanni M., Marzocchi M.
exaly   +6 more sources

Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems

Series in Mathematical Analysis and Applications, 2004
Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory.
Leszek Gasinski, Nikolaos S. Papageorgiou   +1 more
exaly   +6 more sources

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Continuous selections of linear functions and nonsmooth critical point theory

Nonlinear Analysis: Theory, Methods & Applications, 1995
The paper deals with some aspects of the Morse theory for piecewise affine or smooth functions. Let \(f\), \(f_j\), \(j=1, 2, \dots, m\) be real valued continuous functions on \(\mathbb{R}^n\). If \(I(x)= \{i\mid f_i (x)= f(x)\} \neq \emptyset\) for all \(x\in \mathbb{R}^n\), then \(f\) is called a continuous selection (c.s.) of the functions \(f_1 ...
Bartels, Sven G., Kuntz, Ludwig, Scholtes, Stefan   +2 more
openaire   +3 more sources

Buckling of nonlinearly elastic rods in the presence of obstacles treated by nonsmooth critical point theory

Mathematische Annalen, 1998
This paper is devoted to some application of nonsmooth critical point theory to elasticity. In the recent years much interest has been paid to critical points for nonsmooth functionals, especially by the first author and his coworkers. In this paper the authors apply the techniques of modern nonsmooth critical points to nonlinear elasticity, a field ...
Degiovanni, Marco, Schuricht, Friedemann
openaire   +4 more sources

Critical point theory for nonsmooth functionals

Nonlinear Analysis: Theory, Methods & Applications, 2007
The authors develop critical point theory for nonsmooth potentials \(f\colon H^1_0(\Omega)\longrightarrow\mathbb{R}\) of the form \(f(u)=\frac{1}{2}\int_{\Omega}\sum\limits_{i,j=1}^na_{ij}(x,u)D_iuD_ju\,dx-\int_{\Omega}G(x,u)\,dx\). First, the corresponding deformation lemma is proved. Next, a saddle point theorem is proved for functionals defined on a
Liu, Jiaquan, Guo, Yuxia
openaire   +3 more sources

Nonsmooth critical point theory and quasilinear elliptic equations

1995
These lectures are devoted to a generalized critical point theory for nonsmooth functionals and to existence of multiple solutions for quasilinear elliptic equations. If f is a continuous function defined on a metric space, we define the weak slope |df|(u), an extended notion of norm of the Frechet derivative.
CANINO, Annamaria, Degiovanni m.
openaire   +4 more sources

The application of the nonsmooth critical point theory to the stationary electrorheological fluids

Zeitschrift für angewandte Mathematik und Physik, 2016
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Chenyin Qian
openaire   +3 more sources