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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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A bisection algorithm for the numerical Mountain Pass [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2007 We propose a constructive proof for the Ambrosetti-Rabinowitz Mountain Pass Theorem providing an algorithm, based on a bisection method, for its implementation. The efficiency of our algorithm, particularly suitable for problems in high dimensions, consists in the low number of flow lines to be computed for its convergence; for this reason it improves ...
BARUTELLO, Vivina Laura +1 more
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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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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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Numerical Mountain Pass and its Applications [PDF]
PAMM, 2006 AbstractThe mountain pass theorem is an important tool in the calculus of variations and in finding solutions to nonlinear PDEs in general. The mountain pass structure can be exploited numerically, as well. We explain the main ideas on an example of buckling of a cylindrical shell.
Horák, J., Lord, G.J., Peletier, M.A.
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Аж богдын нурууны физик газарзүйн тодорхойлолт
Proceedings of the Mongolian Academy of Sciences, 2017 Mountain Aj Bogd is one of branch mountains the mount systems Mongol Altai, which is located at the middle part of Mongol Altai mountain. Mountain Aj Bogd is similar with surface typology, deposits, form relief, erosion and accumulation process, mountain
Авирмэд Э +1 more
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Abstract and Applied Analysis, 2014 This paper is concerned with the existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects.
Qiongfen Zhang
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Boundary Value Problems, 2018 In this paper, we concern with the following Schrödinger-Poisson system: {−Δu+ϕu=f(x,u),x∈Ω,−Δϕ=u2,x∈Ω,u=ϕ=0,x∈∂Ω, $$ \textstyle\begin{cases} -\Delta u+\phi u = f(x,u) , & x\in\Omega,\\ -\Delta\phi=u^{2}, & x\in\Omega,\\ u=\phi=0, & x \in\partial\Omega, \
Belal Almuaalemi +2 more
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Advances in Difference Equations, 2020 We consider the combined effect of concave–convex nonlinearities on the number of solutions for an indefinite truncated Kirchhoff-type system involving the weight functions.
Qingjun Lou, Yupeng Qin
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Image restoration via Picard's and Mountain-pass Theorems
Electronic Research Archive, 2022 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.
Souad Ayadi , Ozgur Ege
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