Results 11 to 20 of about 1,002 (168)

On the Palais-Smale condition for action integrals

Journal of Functional Analysis, 1992
The author studies the Palais-Smale condition for the action integral \[ f(u) = \int^ 1_ 0 \{\frac 12 | \dot{u}|^ 2 - V(u)\} dt, \quad u\in H^ 1(\mathbb{R}/\mathbb{Z},\mathbb{R}^ n) \] in terms of the potential. This condition was introduced by Palais and Smale in order to find critical points of the action integral.
Majer, Pietro
openaire   +3 more sources

Periodic Solutions of Classical Hamiltonian Systems without Palais–Smale Condition

Journal of Mathematical Analysis and Applications, 2002
The authors consider the second order Hamiltonian system \(\ddot{u}+V_u(t,u)=0\) where \(V:\mathbb R\times\mathbb R^N\rightarrow\mathbb R\) is \({\mathcal{C}}^2\), \(T\)-periodic in \(t\), and \(V_u\) is globally bounded. Further conditions on \(V\) for \(|u|\rightarrow\infty\) are not required.
Fei, Guihua, Kim, Soon-Kyu, Wang, Tixiang   +2 more
openaire   +3 more sources

The multiconfiguration methods in quantum chemistry: Palais–Smale condition and existence of minimizers

Comptes Rendus. Mathématique, 2002
In this Note, we propose a new proof for the existence of a minimum in the multiconfiguration methods in Quantum Chemistry. We use a Palais–Smale condition with Morse-type information, whose proof is based on the Euler–Lagrange equations, written in a simple and useful way.
Lewin, Mathieu
core   +5 more sources

Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems

Electronic Journal of Differential Equations, 1999
When using calculus of variations to study nonlinear elliptic boundary-value problems on unbounded domains, the Palais-Smale condition is not always satisfied.
Chao-Nien Chen, Shyuh-Yaur Tzeng
doaj   +1 more source

On the Palais–Smale condition

Journal of Functional Analysis, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdellaziz Harrabi
openaire   +3 more sources

Ume's u-distance and its relation with both (PS)-condition and coercivity

Electronic Journal of Differential Equations, 2011
In this article, we study the connection between the u-distance and a new Palais-Smale condition of compactness. We compare this Palais-Smale condition with the coercivity.
Georgiana Goga
doaj   +1 more source

Global hyperbolicity and Palais–Smale condition for action functionals in stationary spacetimes

Advances in Mathematics, 2008
In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients of the metric, etc.
CANDELA, Anna Maria, FLORES J. L, SÁNCHEZ M.   +2 more
openaire   +4 more sources

A generalization of Ekeland's variational principle with applications

Electronic Journal of Differential Equations, 2006
In this paper, we establish a variant of Ekeland's variational principle. This result suggest to introduce a generalization of the famous Palais-Smale condition.
Abdel R. El Amrouss, Najib Tsouli
doaj   +1 more source

Global injectivity of C-1 maps of the real plane, inseparable leaves and the Palais-Smale condition [PDF]

, 2015
We study two sufficient conditions that imply global injectivity for a C-1 Map X : R-2 -> R-2 such that its Jacobian at any point of R-2 is not zero. One is based on the notion of half-Reeb component and the other on the Palais-Smale condition.
Llibre, J, Gutierrez, C, Teixeira, MA, Jarque, X   +3 more
core   +3 more sources

Existence of solutions for a double-phase variable exponent equation without the Ambrosetti-Rabinowitz condition

Advances in Nonlinear Analysis, 2023
The article deals with the existence of a pair of nontrivial nonnegative and nonpositive solutions for a nonlinear weighted quasilinear equation in RN{{\mathbb{R}}}^{N}, which involves a double-phase general variable exponent elliptic operator A{\bf{A}}.
Liu Jingjing, Pucci Patrizia
doaj   +1 more source