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Existence of nontrivial solutions for Schrodinger-Kirchhoff equations with indefinite potentials
Electronic Journal of Differential Equations, 2023 Shuai Jiang, Li-Feng Yin
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Multiple solutions of differential equations without the Palais-Smale condition
Mathematische Annalen, 1982 openaire +2 more sources
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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\
David G Costa
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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 ...
Hwai-Chiuan Wang
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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.
Chengkui Zhong
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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.
Michel Willem +2 more
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On the relation between the weak Palais–Smale condition and coercivity given by Zhong
Nonlinear Analysis: Theory, Methods & Applications, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tomonari Suzuki
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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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