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Equilibrium Problems Via the Palais-Smale Condition
2006Inspired by some results from nonsmooth critical point theory, we propose in this paper to study equilibrium problems by means of a general Palais-Smale condition adapted to bifunctions. We introduce the notion of critical points for equilibrium problems and we give some existence results for (EP) with lack of compacity.
Ouayl Chadli, Zaki Chbani, Hassan Riahi
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On resonance Hamiltonian systems without the Palais–Smale condition
Nonlinear Analysis: Theory, Methods & Applications, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Palais–Smale conditions for the Yang–Mills functional
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988SynopsisWe 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
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Palais-Smale condition for chiral fields
2020It is considered the problem of critical points for the functional \(f(u)\), \(u\in E\) on the surface \(\{u\in E: F(u)= 0\}\) with essentially nonlinear \(F: E\to E_1\). In a variational formulated case of the problem of spherical fields in the bounded domains a Palais-Smale compactness condition is proved.
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Limit Cases of the Palais-Smale Condition
1990Condition (P.-S.) may seem rather restrictive. Actually, as Hildebrandt [4; p. 324] records, for quite a while many mathematicians felt convinced that inspite of its success in dealing with one-dimensional variational problems like geodesics (see Birkhoff’s Theorem I.4.4, for example, or Palais’ [3] work on closed geodesics), the Palais-Smale condition
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Mountain Pass Theorems, Deformation Theorems, and Palais-Smale Conditions
2001Let E be a Banach space, X ⊂ E be an open subset, f ∈ C 1 (X, R) be a functional and $$\begin{array}{*{20}{c}} {K = \left\{ {x \in X:f'\left( x \right) = 0} \right\},} \\ {{K_c} = \left\{ {x \in X:f\left( x \right) = c,f'\left( x \right) = 0} \right\}} \end{array}$$ are the sets of critical points of f.
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