Sandwich systems
type: Item
instance of: scholarly article
title: Sandwich systems
zbMATH Open document ID: 1263.35106
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-01-14T00:00:00Z
review text: The paper under review deals with some interesting and modern topics concerning the qualitative analysis of energy functionals that are naturally associated to various classes of stationary problems. If the energy functional \(G\) is bounded from below, one can show that there is a Palais-Smale sequence \((u_n)\) satisfying \(G(u_n) \rightarrow a\) and \(G'(u_n)\rightarrow 0\), where \( a = \inf G\). If the sequence has a convergent subsequence, this will produce a minimum. However, when the functional is not semibounded, the matter is more complicated and can have different features. That is why different devices must be used according to the various difficulties that can occur (mountain pass geometry, saddle point structure, linking, restriction to the Nehari manifold, Benci-Rabinowitz theorem, etc.). In the present paper it is developed an approach that produces Cerami-type sequences for functionals which are not semibounded. They are not quite Cerami sequences, but they are just as effective in many applications, as pointed out in the last part of this paper.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6125368
zbMATH Keywords: critical point theory
zbMATH Keywords: variational methods
zbMATH Keywords: saddle point theory
zbMATH Keywords: semilinear differential equations
author: Martin Schechter
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.09.022
OpenAlex ID: W4205871035
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DOI: 10.1016/J.JMAA.2012.09.022
description: scientific article; zbMATH DE number 6125368