Results 11 to 20 of about 3,788 (155)
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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Multiple critical points theorems without the Palais–Smale condition
Journal of Mathematical Analysis and Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gabriele Bonanno
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Periodic Solutions of Classical Hamiltonian Systems without Palais–Smale Condition
Journal of Mathematical Analysis and Applications, 2002 The authors consider the second order Hamiltonian system \(\ddot{u}+V_u(t,u)=0\) where \(V:\mathbb R\times\mathbb R^N\rightarrow\mathbb R\) is \({\mathcal{C}}^2\), \(T\)-periodic in \(t\), and \(V_u\) is globally bounded. Further conditions on \(V\) for \(|u|\rightarrow\infty\) are not required.
Fei, Guihua +2 more
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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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Advances in Nonlinear Analysis, 2023 The article deals with the existence of a pair of nontrivial nonnegative and nonpositive solutions for a nonlinear weighted quasilinear equation in RN{{\mathbb{R}}}^{N}, which involves a double-phase general variable exponent elliptic operator A{\bf{A}}.
Liu Jingjing, Pucci Patrizia
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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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Nodal solutions for the Choquard equation [PDF]
, 2016 We consider the general Choquard equations $$ -\Delta u + u = (I_\alpha \ast |u|^p) |u|^{p - 2} u $$ where $I_\alpha$ is a Riesz potential. We construct minimal action odd solutions for $p \in (\frac{N + \alpha}{N}, \frac{N + \alpha}{N - 2})$ and ...
Ghimenti, Marco, Van Schaftingen, Jean
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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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