Results 151 to 160 of about 13,124,526 (179)

Zhang equivalency of inequation-to-inequation type for constraints of redundant manipulators. [PDF]

Heliyon
Wu D, Zhang Y.
europepmc   +1 more source

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   +4 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.
Marco Degiovanni
exaly   +5 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 ...
Marco Marzocchi, Marco Degiovanni
exaly   +5 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 Gasiński, Nikolaos S Papageorgiou   +1 more
exaly   +5 more sources

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Nonsmooth critical point theory and applications to the spectral graph theory

Science China Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sihong Shao, Dong Zhang
exaly   +3 more sources

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 ...
Stefan Scholtes, Ludwig Kuntz
exaly   +2 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
Yuxia Guo, Jiaquan Liu
exaly   +2 more sources