Results 141 to 150 of about 9,842 (165)

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
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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
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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
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Linking-Type Results in Nonsmooth Critical Point Theory and Applications

Set-Valued and Variational Analysis, 2016
The authors extend Schechter's critical point alternative for \(C^1\) functions on closed balls in Hilbert spaces to locally Lipschitz functions on closed balls in reflexive Banach spaces. The key idea is the use of duality mappings. Applications to differential inclusions with \(p\)-Laplacian are given.
Nicuşor Costea, Mihály Csirik, Csaba Varga   +2 more
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Nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequalities

Nonlinear Analysis: Theory, Methods & Applications, 2005
The authors construct a constrained nonsmooth critical point theory for locally Lipschitz functionals that are defined only on closed convex subsets of reflexive Banach spaces. This extends Struwe's corresponding theory in the smooth case. The basic technical tool in the extension is represented by the notion of generalized gradient in the sense of ...
Kyritsi, Sophia Th., Papageorgiou, Nikolaos S.   +1 more
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Three Solutions for a Partial Differential Inclusion Via Nonsmooth Critical Point Theory

Set-Valued and Variational Analysis, 2010
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Antonio Iannizzotto
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Three anti-periodic solutions for second-order impulsive differential inclusions via nonsmooth critical point theory

Nonlinear Analysis: Theory, Methods & Applications, 2012
The main result of the paper establishes the existence of at least three anti-periodic solutions for a second-order impulsive differential inclusion. The authors develop a novel variational approach in the context of impulsive differential inclusions.
Tian, Yu, Henderson, Johnny
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Multiplicity result for some nonlocal anisotropic equation via nonsmooth critical point theory approach

Applied Mathematics and Computation, 2011
The author considers the following problem for the unknown function \(u\): \[ \alpha'(\Psi(u))\left[-\text{div}(A(x,u)|\nabla u|^{p(x)-2}\nabla u)+\frac{A'_t(x,u)}{p(x)}|\nabla u|^{p(x)}+|u|^{p(x)-2}u\right]=f(x,u) \] in \(\mathbb{R}^n \), \noindent where \(\Psi(\cdot)\) represents a suitable integral operator, and \(A\) and \(f\) are symmetric in ...
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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
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Multiplicity of Nontrivial Solutions for Boundary Value Problem for Impulsive Fractional Differential Inclusions Via Nonsmooth Critical Point Theory

Fractional Calculus and Applied Analysis, 2015
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Nemat Nyamoradi
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