On the Poincaré-Hopf Theorem for Functionals Defined on Banach Spaces

DOI10.1515/ans-2009-0406zbMath1187.58016OpenAlexW63842145MaRDI QIDQ3645989

Silvia Cingolani, Marco Degiovanni

Publication date: 18 November 2009

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2009-0406

zbMATH Keywords

nonsmooth critical point theorycritical growthquasilinear elliptic problemsPoincaré-Hopf theorem

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Nonlinear boundary value problems for linear elliptic equations (35J65) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (13)

Amann-Zehnder type results for \(p\)-Laplace problems ⋮ Critical group estimates for nonregular critical points of functionals associated with quasilinear elliptic equations ⋮ Weighted Sobolev spaces and Morse estimates for quasilinear elliptic equations ⋮ Corrigendum to ``The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systems ⋮ On local Morse theory for \(p\)-area functionals, \(p > 2\) ⋮ Floer homology in the cotangent bundle of a closed Finsler manifold and noncontractible periodic orbits ⋮ Methods of infinite dimensional Morse theory for geodesics on Finsler manifolds ⋮ On the critical polynomial of functionals related to \(p\)-area (for \(1 < p < \infty\)) and \(p\)-Laplace \((1 < p\leq2)\) type operators ⋮ Towards a Morse theory on Banach spaces via ultrafunctions ⋮ Unnamed Item ⋮ Morse theory methods for a class of quasi-linear elliptic systems of higher order ⋮ Parameterized splitting theorems and bifurcations for potential operators. I: Abstract theory ⋮ Critical groups at zero and multiple solutions for a quasilinear elliptic equation

Cites Work

• Unnamed Item
• The generalized Morse lemma and the Euler characteristic on Banach manifolds
• A new approach to the Morse-Conley theory and some applications
• Buckling of nonlinearly elastic rods in the presence of obstacles treated by nonsmoth critical point theory
• A critical point theory for nonsmooth functionals
• Homotopical stability of isolated critical points of continuous functionals
• Mountain pass theorems and global homeomorphism theorems
• Metric critical point theory. I: Morse regularity and homotopic stability of a minimum
• Fixed point theory and nonlinear problems

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