Advances in Differential Equations

Location and critical groups of critical points in Banach spaces with an application to nonlinear eigenvalue problems

Thomas Bartsch and Zhaoli Liu

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Abstract

We develop critical-point theory in Banach spaces in order to find critical points inside or outside of given convex subsets of the space. In addition to localizing critical points we also obtain results on their critical groups. The abstract theory can be applied to $p$-Laplacian equations in order to prove the existence of multiple sign-changing solutions.

Article information

Source
Adv. Differential Equations Volume 9, Number 5-6 (2004), 645-676.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867939

Mathematical Reviews number (MathSciNet)
MR2099975

Zentralblatt MATH identifier
1100.58005

Subjects
Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 35J25: Boundary value problems for second-order elliptic equations 35J60: Nonlinear elliptic equations 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory

Citation

Bartsch, Thomas; Liu, Zhaoli. Location and critical groups of critical points in Banach spaces with an application to nonlinear eigenvalue problems. Adv. Differential Equations 9 (2004), no. 5-6, 645--676. https://projecteuclid.org/euclid.ade/1355867939.


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