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A Strong Form of the Mountain Pass Theorem and Application
Mathematical Sciences Research Institute Publications, 1988Variational methods are a strong tool in proving existence of solutions of differential equations. In this paper we prove a strong form of the mountain pass theorem which was prompted by the need of a theorem which, besides an existence statement for critical points, gives in addition information about the “fine structure” of the functional near to ...
Hofer H
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The Mountain-Pass Theorem [PDF]
, 2007 Roughly speaking, the basic idea behind the so-called minimax method is the following: Find a critical value of a functional ϕ ∈ C1 (X, ℝ) as a minimax (or maximin) value c ∈ ℝ of ϕ over a suitable class A of subsets of X: $$ c = \mathop {\inf }\limits_{A \in \mathcal{A}} \mathop {\sup }\limits_{u \in A} \phi \left( u \right). $$
David G. Costa
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A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations [PDF]
Journal of Functional Analysis, 2005 For an even functional on a Banach space, the symmetric mountain pass lemma gives a sequence of critical values which converges to zero. Under the same assumptions on the functional, this paper establishes a new critical point theorem which provides a ...
Ryuji Kajikiya
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Mountain Pass solutions for non-local elliptic operators [PDF]
Journal of Mathematical Analysis and Applications, 2012 The purpose of this paper is to study the existence of solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions.
Enrico Valdinoci, Raffaella Servadei
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Application of a Variant of Mountain Pass Theorem in Modeling Real Phenomena [PDF]
Mathematics, 2022 Mountain Pass Theorem (MPT) is an important result in variational methods with multiple applications in partial differential equations involved in mathematical physics. Starting from a variant of MPT, a new result concerning the existence of the solution
Irina Meghea
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Positive mountain pass solutions for a semilinear elliptic equation with a sign-changing weight function [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2006 We use the mountain pass theorem to study the existence and multiplicity of positive solutions of the generalisation of the well-known logistic equation -?u=?g(x)u(x)(1-u(x)) with Dirichlet boundary conditions to the case where g changes sign.
G A Afrouzi
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An Application of a Mountain Pass Theorem
Acta Mathematica Sinica, English Series, 2002The present paper is devoted to study the following Dirichlet problem: \[ -\Delta u=f(x,u), \quad x\in\Omega,\;u\in H^1_0(\Omega),\tag{1} \] where \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^N\), with \(f(x,t)\) asymptotically linear in \(t\) at infinity.
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Minimization and Mountain-Pass Theorems
2001In this introductory chapter, we consider the concept on differentiability of mappings in Banach spaces, Frechet and Gâteaux derivatives, secondorder derivatives and general minimization theorems. Variational principles of Ekeland [Ek1] and Borwein & Preiss [BP] are proved and relations to the minimization problem are given. Deformation lemmata, Palais—
Maria do Rosário Grossinho +1 more
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2003
This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a ...
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This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a ...
openaire +1 more source