Results 11 to 20 of about 781 (177)
The structure of the critical set in the mountain pass theorem [PDF]
Transactions of the American Mathematical Society, 1987 We show that the critical set generated by the Mountain Pass Theorem of Ambrosetti and Rabinowitz must have a well-defined structure. In particular, if the underlying Banach space is infinite dimensional then either the critical set contains a saddle point of mountain-pass type, or the set of local minima intersects at least
PUCCI, Patrizia, J. SERRIN
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GENERAL QUASILINEAR PROBLEMS INVOLVING \(p(x)\)-LAPLACIAN WITH ROBIN BOUNDARY CONDITION
Ural Mathematical Journal, 2020 This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving \(p(x)\)-Laplace type equation, namely $$ \left\{\begin{array}{lll} -\mathrm{div}\, (a(| \nabla u|^{p(x)})| \nabla u|^{p(x)-2} \nabla u ...
Hassan Belaouidel +2 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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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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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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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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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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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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