Results 11 to 20 of about 3,762 (154)
Global inversion via the Palais-Smale condition
Discrete & Continuous Dynamical Systems - A, 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 \(w\in \mathbb R^n\).
Nollet, Scott, Xavier, Frederico
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ON THE PALAIS-SMALE CONDITION FOR NONDIFFERENTIABLE FUNCTIONALS
Taiwanese Journal of Mathematics, 2000 In this paper the author studies the relations between some extensions to nonsmooth functionals of the classical Palais-Smale (PS) compactness condition for smooth functionals. In particular the relations between some results of K. C. Chang and other results by Costa and Goncalves are presented.
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Global hyperbolicity and Palais–Smale condition for action functionals in stationary spacetimes
Advances in Mathematics, 2008 In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients of the metric, etc.
CANDELA, Anna Maria +2 more
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A concave-convex problem with a variable operator [PDF]
, 2017 We study the following elliptic problem $-A(u) = \lambda u^q$ with Dirichlet boundary conditions, where $A(u) (x) = \Delta u (x) \chi_{D_1} (x)+ \Delta_p u(x) \chi_{D_2}(x)$ is the Laplacian in one part of the domain, $D_1$, and the $p-$Laplacian (with ...
Molino, Alexis, Rossi, Julio D.
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Existence of Positive Solutions of Semilinear Biharmonic Equations
Abstract and Applied Analysis, 2014 This paper is concerned with the existence of positive solutions of semilinear biharmonic problem whose associated functionals do not satisfy the Palais-Smale condition.
Yajing Zhang, Yinmei Lü, Ningning Wang
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Advanced Nonlinear Studies, 2020 In this paper we establish a new critical point theorem for a class of perturbed differentiable functionals without satisfying the Palais–Smale condition.
Bahrouni Anouar +2 more
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Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity [PDF]
, 2014 This paper deals with the existence and the asymptotic behavior of non-negative solutions for a class of stationary Kirchhoff problems driven by a fractional integro-differential operator $\mathcal L_K$ and involving a critical nonlinearity.
Autuori, Giuseppina +2 more
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A Viscosity Method for the Min-Max Construction of Closed Geodesics [PDF]
, 2015 We present a viscosity approach to the min-max construction of closed geodesics on compact Riemannian manifolds of arbitrary dimension. We also construct counter-examples in dimension $1$ and $2$ to the $\varepsilon$-regularity in the convergence ...
Michelat, Alexis, Rivière, Tristan
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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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Journal of Functional Analysis, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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