2002
DOI: 10.1090/s0273-0979-02-00929-1
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Selected new aspects of the calculus of variations in the large

Abstract: Abstract. We discuss some of the recent developments in variational methods while emphasizing new applications to nonlinear problems. We touch on several issues: (i) the formulation of variational set-ups which provide more information on the location of critical points and therefore on the qualitative properties of the solutions of corresponding Euler-Lagrange equations; (ii) the relationships between the energy of variationally generated solutions, their Morse indices, and the Hausdorff measure of their noda… Show more

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Cited by 149 publications
(88 citation statements)
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“…We refer moreover to the recent papers [2] and [4] for a complete survey of the topic. The authors of [4] deal with the problem…”
Section: Introductionmentioning
confidence: 99%
“…We refer moreover to the recent papers [2] and [4] for a complete survey of the topic. The authors of [4] deal with the problem…”
Section: Introductionmentioning
confidence: 99%
“…A. Ferrero and F. Gazzola [8] also obtained some results for problem (1.1). For other relevant papers see [1,3,6,7,10,12], and the references therein.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…For the homogeneous case, Ben-Naoum, Troestler and Willem [Ben-Naoum et al 1994] proved the existence of a nonconstant solution. For the case T = 2π , Theorem 1.7, with substantially stronger hypotheses, was proved by Nirenberg; see [Ekeland and Ghoussoub 2002]. Among other things, they assumed…”
Section: Then the Systemmentioning
confidence: 97%