Results 1 to 10 of about 717 (159)
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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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 +2 more
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A Mountain Pass Theorem for a Suitable Class of Functions
Rocky Mountain Journal of Mathematics, 2009 In this article, a mountain pass theorem is obtained for a functional of the form \(J=\Phi-\Psi\) defined on a reflexive real Banach space, where \(\Phi\) and \(\Psi\) are continuously Gâteau differentiable functions, \(\Phi\) is convex, and \(J_M = \Phi-\Psi_M\) satisfies the Palais--Smale condition (PS)\(_c\) with \(\Psi_M\) the cut-off function at a
Gabriele Bonanno
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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 ...
Patrizia Pucci, James Serrin
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A compression type mountain pass theorem in conical shells
Journal of Mathematical Analysis and Applications, 2008 Let \(X\subset H\equiv H'\subset X'\) be the chain of two Hilbert spaces \(X\) and \(H\) with norms \(| \cdot | \) and \(\| \cdot \| \). Let \(0\neq K\subset X\) be a nonempty closed convex set such that \(\lambda u\in K\) \(\forall u\in K\) and \(\lambda\geq0\). The author studies critical points of a functional \(E\in C^1(X,\mathbb R) \) such that \((
Radu Precup
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Multiple solutions for a quasilinear Choquard equation with critical nonlinearity
Open Mathematics, 2021 In the present work, we are concerned with the multiple solutions for quasilinear Choquard equation with critical nonlinearity in RN{{\mathbb{R}}}^{N}.
Li Rui, Song Yueqiang
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On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent
Journal of Function Spaces, 2022 In this paper, we deal with p-Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial ...
Mohammed El Mokhtar ould El Mokhtar
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Advances in Difference Equations, 2019 In this paper, we prove a new quantitative deformation lemma, and then gain a new mountain pass theorem in Hilbert spaces. By using the new mountain pass theorem, we obtain the new existence of two nontrivial periodic solutions for a class of nonlinear ...
Liang Ding, Jinlong Wei, Shiqing Zhang
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Existence and multiplications of solutions for a class of equation with a non-smooth potential [PDF]
Journal of Hyperstructures, 2015 This paper deals with the existence and multiplicity of solutions for a class of nonlocal p−Kirchhoff problem. Using the mountain pass theorem and fountain theorem, we establish the existence of at least one solution and infinitely many solutions for a ...
Fariba Fattahi, M. Alimohammady
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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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