Results 21 to 30 of about 1,117,308 (199)
A variant of mountain pass theorem
Differential and Integral Equations, 2013 An existence result for a critical point of mountain-pass type, where the classical Palais--Smale condition is not required, is presented. A multiple-critical-point result is then obtained. As an application, the existence of two positive classical solutions for two-point boundary-value problems, without assuming any asymptotic condition on the ...
Bonanno, Gabriele, D'Aguì, Giuseppina
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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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The mountain pass theorem in terms of tangencies
, 2021 This paper addresses the Mountain Pass Theorem for locally Lipschitz functions on finite-dimensional vector spaces in terms of tangencies. Namely, let $f \colon \mathbb R^n \to \mathbb R$ be a locally Lipschitz function with a mountain pass geometry.
Dinh, Si Tiep, Pham, Tien Son
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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 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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پژوهشهای ریاضی, 2022 We investigate the existence of a weak nontrivial solution for the following problem. Our analysis is generally bathed on discussions of variational based on the Mountain Pass theorem and some recent theories one the generalized Lebesgue-Sobolev space ...
Atieh Ramzannia Jalali +1 more
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Multiplicity of positive solutions for second order quasilinear equations [PDF]
Mathematica Bohemica, 2020 We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
Dahmane Bouafia +2 more
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Abstract and Applied Analysis, 2013 We investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with local superquadratic potential by using the Mountain Pass Theorem and the Fountain Theorem, respectively.
Ying Lv, Chun-Lei Tang
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Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems
Advances in Mathematical Physics, 2020 We consider the following double phase problem with variable exponents: −div∇upx−2∇u+ax∇uqx−2∇u=λfx,u in Ω,u=0, on ∂Ω. By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some ...
Jie Yang, Haibo Chen, Senli Liu
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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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