Results 11 to 20 of about 729 (179)
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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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
D. Averna, BONANNO, Gabriele
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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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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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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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Journal of Function Spaces, 2015 This paper is concerned with the following nonlinear second-order nonautonomous problem: ü(t)+q(t)u̇(t)-∇K(t,u(t))+∇W(t,u(t))=0, where t∈R, u∈RN, and K, W∈C1(R×RN,R) are not periodic in t and q:R→R is a continuous function and Q(t)=∫0tq(s)ds with lim|t|
Qiongfen Zhang, Yuan Li
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A Mountain Pass-type Theorem for Vector-valued Functions [PDF]
Set-Valued and Variational Analysis, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bednarczuk, E +2 more
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