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MOUNTAIN PASS THEOREM WITH INFINITE DISCRETE SYMMETRY

MOUNTAIN PASS THEOREM WITH INFINITE DISCRETE SYMMETRY
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Minimization and Mountain-Pass Theorems

2001
In 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, Stepan Agop Tersian   +1 more
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The mountain pass theorem in terms of tangencies

Journal of Mathematical Analysis and Applications
Sĩ Tiệp Đinh, Tiến-Sơn Phạm
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Mountain pass theorems without Palais–Smale conditions

Journal of Mathematical Sciences, 2009
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An Application of a Mountain Pass Theorem

Acta Mathematica Sinica, English Series, 2002
The 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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The Mountain Pass Theorem

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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The Mountain-Pass Theorem

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: $$ c = \mathop {\inf }\limits_{A \in \mathcal{A}} \mathop {\sup }\limits_{u \in A} \phi \left( u \right). $$
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Mountain Pass Theorems, Deformation Theorems, and Palais-Smale Conditions

2001
Let E be a Banach space, X ⊂ E be an open subset, f ∈ C 1 (X, R) be a functional and $$\begin{array}{*{20}{c}} {K = \left\{ {x \in X:f'\left( x \right) = 0} \right\},} \\ {{K_c} = \left\{ {x \in X:f\left( x \right) = c,f'\left( x \right) = 0} \right\}} \end{array}$$ are the sets of critical points of f.
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p-Laplacian Type Equations Via Mountain Pass Theorem in Cerami Sense

Qualitative Theory of Dynamical Systems
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Vanterler da C. Sousa, J., Nyamoradi, Nemat, Frederico, Gastão F.   +2 more
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A VARIANT OF THE MOUNTAIN-PASS THEOREM

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'AGUI', GIUSEPPINA
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