Results 11 to 20 of about 24,259 (189)
Relations between the mountain pass theorem and local minima
Advances in Nonlinear Analysis, 2012 Existence results of two critical points for functionals unbounded from below are established after pointing out a characterization of the mountain pass geometry. Applications to elliptic Dirichlet problems are then presented.
Bonanno Gabriele
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Journal of Differential Equations, 1985 In this paper we establish a new version of the well-known theorem of Ambrosetti and Rabinowitz on the existence of critical points for functionals \(I: X\to {\mathbb{R}}\) of class \(C^ 1\) on a real Banach space X. As usual, a compactness condition of Palais-Smale type is assumed throughout, including a version particularly suited to the periodic ...
PUCCI, Patrizia, J. SERRIN
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A Variant of the Mountain Pass Theorem and Variational Gluing [PDF]
Milan Journal of Mathematics, 2020 AbstractThis paper surveys some recent work on a variant of the Mountain Pass Theorem that is applicable to some classes of differential equations involving unbounded spatial or temporal domains. In particular its application to a system of semilinear elliptic PDEs on $$R^n$$ R n and to a family of Hamiltonian systems involving double well ...
Piero Montecchiari, Paul H. Rabinowitz
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Extensions of the mountain pass theorem
Journal of Functional Analysis, 1984 The paper contains a number of extensions of the mountain pass lemma of \textit{A. Ambrosetti} and \textit{P. H. Rabinowitz} [(*) ibid. 14, 349-381 (1973; Zbl 0273.49063)]. The lemma gives sufficient conditions for the existence of critical points of continuously Fréchet differentiable functionals \(I: X\to {\mathbb{R}}\) on a real Banach space X.
PUCCI, Patrizia, J. SERRIN
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MOUNTAIN PASS THEOREM WITH INFINITE DISCRETE SYMMETRY
, 2016 The Mountain Pass Theorem is one of the fundamental results of calculus of variations and nonlinear analysis, used to establish the existence of critical points (of higher index) with numerous applications in many areas of mathematics. The paper under review extends the classical formulation of this theorem to an equivariant setting, regarding ...
Bárcenas, Noé
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Image restoration via Picard's and Mountain-pass Theorems
Electronic Research Archive, 2022 <abstract><p>In this work, we present existence results for some problems which arise in image processing namely image restoration. Our essential tools are Picard's fixed point theorem for a strict contraction and Mountain-pass Theorem for critical point.</p></abstract>
Souad Ayadi, Özgür Ege
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Mountain pass theorems and global homeomorphism theorems [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1994 We show that mountain-pass theorems can be used to derive global homeomorphism theorems. Two new mountain-pass theorems are proved, generalizing the “smooth” mountain-pass theorem, one applying in locally compact topological spaces, using Hofer’s concept of mountain-pass point, and another applying in complete metric spaces, using a generalized notion ...
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A Mountain-Pass Theorem for Asymptotically Conical Self-Expanders
Peking Mathematical Journal, 2022 We develop a min-max theory for asymptotically conical self-expanders of mean curvature flow. In particular, we show that given two distinct strictly stable self-expanders that are asymptotic to the same cone and bound a domain, there exists a new asymptotically conical self-expander trapped between the two.
Jacob Bernstein, Lu Wang
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Nontrivial Solutions for Asymmetric Kirchhoff Type Problems
Abstract and Applied Analysis, 2014 We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and −∞ in ℝN(N=2,3). Namely, it is 4-linear at −∞ and 4-superlinear at +∞.
Ruichang Pei, Jihui Zhang
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Existence and multiplicity of nontrivial solutions for poly-Laplacian systems on finite graphs
Boundary Value Problems, 2022 In this paper, we investigate the existence and multiplicity of nontrivial solutions for poly-Laplacian system on a finite graph G = ( V , E ) $G=(V, E)$ , which is a generalization of the Yamabe equation on a finite graph.
Xuechen Zhang +3 more
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