Advances in Differential Equations

Morse index estimates for continuous functionals associated with quasilinear elliptic equations

Sergio Lancelotti

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Abstract

A result of Amann-Zehnder type for quasilinear elliptic equations is proved when the origin is a degenerate critical point. For this purpose, the critical groups of the associated continuous functionals are studied. An adaptation of the Generalized Morse Lemma is proved.

Article information

Source
Adv. Differential Equations Volume 7, Number 1 (2002), 99-128.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651877

Mathematical Reviews number (MathSciNet)
MR1867706

Zentralblatt MATH identifier
1035.58010

Subjects
Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 35J60: Nonlinear elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations 47J30: Variational methods [See also 58Exx]

Citation

Lancelotti, Sergio. Morse index estimates for continuous functionals associated with quasilinear elliptic equations. Adv. Differential Equations 7 (2002), no. 1, 99--128. https://projecteuclid.org/euclid.ade/1356651877.


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