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Origin and evolution of the Palais–Smale condition in critical point theory

Journal of Fixed Point Theory and Applications, 2010
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Jean Mawhin, Michel Willem, Mawhin Jean   +2 more
exaly   +3 more sources

On the relation between the weak Palais–Smale condition and coercivity given by Zhong [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2008
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Tomonari Suzuki
exaly   +4 more sources

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The palais-smale condition versus coercivity

Nonlinear Analysis: Theory, Methods & Applications, 1991
Let \(\phi: X\to\mathbb R\) be a given functional on a Banach space \(X\). \(\phi\) is said to be coercive if \(\phi(u)\to +\infty\) as \(\| u\| \to \infty\). This is equivalent to saying that for each \(d\in\mathbb R\), the set \(\Phi^ d=\{u\in X: \phi(u)\leq d\}\) is bounded. A differentiable functional (in the sense of Fréchet) \(\phi: X\to\mathbb R\
David G Costa
exaly   +2 more sources

A Necessary and Sufficient Condition for Palais--Smale Conditions

SIAM Journal on Mathematical Analysis, 1999
Let \(\Omega\) be an arbitrary domain in \({\mathbb{R}}^N\), \(N\geq 2\). Denote \(2^*= +\infty\) if \(N=2\), and \(2^*=2N/(N-2)\) for \(N\geq 3\). The paper establishes a necessary and sufficient condition for the Palais-Smale property related to the boundary value problem \(-\Delta u+u=|u|^{p-2}u\) in \(\Omega\), subject to the Dirichlet condition ...
Hwai-Chiuan Wang
exaly   +2 more sources

A weak nonsmooth palais-smale condition and coercivity

Rendiconti Del Circolo Matematico Di Palermo, 2000
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Nikolaos C Kourogenis, Nikolaos S Papageorgiou, Papageorgiou Nikolaos S   +2 more
exaly   +2 more sources

Palais–Smale condition and global attractor for gradient system

Nonlinear Analysis: Theory, Methods & Applications, 2008
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Yansheng Zhong, Chengkui Zhong
exaly   +2 more sources

The Palais–Smale conditions for the Yang–Mills functional

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988
SynopsisWe consider the Yang–Mills functional denned on connections on a principal bundle over a compact Riemannian manifold of dimension 2 or 3. It is shown that if we consider the Yang–Mills functional as being defined on an appropriate Hilbert manifold of orbits of connections under the action of the group of principal bundle automorphisms, then the
D. R. Wilkins
openaire   +2 more sources

A linear perturbed Palais-Smale condition for lower semicontinuous functions on Banach spaces

Acta Mathematica Sinica, English Series, 2008
NSFC [10471114]This paper introduces a notion of linear perturbed Palais-Smale condition for real-valued functions on Banach spaces. In terms of strongly exposed points, it presents a characterization which guarantees linear perturbed Palais-Smale ...
Liu, X. Y., Cheng, L. X., Zuo, M. F., 程立新   +3 more
exaly   +1 more source

The Palais-Smale Condition and Mañé's Critical Values

Annales Henri Poincaré, 2000
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Contreras, G., Iturriaga, R., Paternain, G. P., Paternain, M.   +3 more
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Note on a general Palais–Smale condition

Nonlinear Analysis: Theory, Methods & Applications, 2011
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