Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems [PDF]
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
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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
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Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition [PDF]
, 2020 This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the ...
Elliot Tonkes
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Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type
Abstract and Applied Analysis, 2013 We prove a theorem on the existence and uniqueness of a solution as well as on a sensitivity (i.e., differentiable dependence of a solution on a functional parameter) of a fractional integrodifferential Cauchy problem of Volterra type.
Dariusz Idczak +2 more
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On the relation between the weak Palais-Smale condition and coercivity given by Zhong [PDF]
, 2008 In this paper, we discuss Zhong’s result of that the weak Palais-Smale condition implies coercivity under some assumption in [Nonlinear Anal., 29 (1997), 1421–1431]. We also give a simple proof of Zhong’s result.
00303173 +6 more
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Global injectivity of C-1 maps of the real plane, inseparable leaves and the Palais-Smale condition
, 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 +3 more
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New Periodic Solutions for the Singular Hamiltonian System
Abstract and Applied Analysis, 2014 By use of the Cerami-Palais-Smale condition, we generalize the classical Weierstrass minimizing theorem to the singular case by allowing functions which attain infinity at some values. As an application, we study certain singular second-order Hamiltonian
Yi Liao
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Origin and evolution of the Palais-Smale condition in critical point theory
, 2010 In 1963–64, Palais and Smale have introduced a compactness condition, namely condition (C), on real functions of class C 1 defined on a Riemannian manifold modeled upon a Hilbert space, in order to extend Morse theory to this frame and study nonlinear ...
Michel Willem +3 more
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On a functional satisfying a weak Palais-Smale condition
, 2014 In this paper we study a quasilinear elliptic problem whose functional satisfies a weak version of the well known Palais-Smale condition.
AZZOLLINI, ANTONIO, Antonio Azzollini
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On Palais-Smale sequences for H-Systems: some examples
, 2006 We exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up ...
MUSINA, Roberta, CALDIROLI P
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