Results 101 to 110 of about 218 (139)
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The Palais-Smale Condition Versus Coercivity
Nonlinear Analysis: Theory, Methods & Applications, 1991Let \(\phi: X\to\mathbb R\) 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\
Costa, David G. +1 more
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A Necessary and Sufficient Condition for Palais--Smale Conditions
SIAM Journal on Mathematical Analysis, 1999Let \(\Omega\) 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 ...
Kuan-Ju Chen
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A Weak Nonsmooth Palais-Smale Condition and Coercivity
Rendiconti Del Circolo Matematico Di Palermo, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nikolaos S. Papageorgiou +1 more
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Palais–Smale Condition and Global Attractor for Gradient System
Nonlinear Analysis: Theory, Methods & Applications, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yansheng Zhong, Cheng-Kui Zhong
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On a Functional Satisfying a Weak Palais-Smale Condition
Discrete and Continuous Dynamical Systems, 2014 In this paper we study a quasilinear elliptic problem whose functional satisfies a weak version of the well known Palais-Smale condition. An existence result is proved under general assumptions on the nonlinearities.
Antonio Azzollini
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The Palais-Smale Condition and Mañé's Critical Values
Annales Henri Poincaré, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Contreras, G. +3 more
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Global Inversion via the Palais-Smale Condition
Discrete and Continuous Dynamical Systems, 2002 The paper concerns the problem when a local diffeomorphism \(f:\mathbb R^n\to\mathbb R^n\) is bijective. Let \(g\) be a complete Riemannian metric on \(\mathbb R^n\) and \(h:\mathbb R^n\to\mathbb R\) be a smooth function. Let \(\Delta ^{(g)}h\) be its gradient relative to \(g\) i.e. \(g_x(\Delta ^{(g)}h,w)=dh_x(w)\) for all \(w\in \mathbb R^n\).
Scott Nollet
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Origin and Evolution of the Palais–Smale Condition in Critical Point Theory
Journal of Fixed Point Theory and Applications, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean Mawhin, Michel Willem
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Nonstandard Palais-Smale conditions
2007We present nonstandard versions of the Palais-Smale condition (PS) below, some of them generalizations, but still sufficient to prove Mountain Pass Theorems, which are quite important in Critical Point Theory.
Natália Martins, Vítor Neves
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2014
In this section we prove a Palais–Smale condition for minimizing sequences of blowup solutions to the defocusing energy-critical NLS. It was already observed in [5, 13] that such minimizing sequences have good tightness and equicontinuity properties.
Herbert Koch +2 more
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In this section we prove a Palais–Smale condition for minimizing sequences of blowup solutions to the defocusing energy-critical NLS. It was already observed in [5, 13] that such minimizing sequences have good tightness and equicontinuity properties.
Herbert Koch +2 more
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