Advances in Differential Equations
- Adv. Differential Equations
- Volume 9, Number 5-6 (2004), 645-676.
Location and critical groups of critical points in Banach spaces with an application to nonlinear eigenvalue problems
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.
Adv. Differential Equations Volume 9, Number 5-6 (2004), 645-676.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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.