A Morse-Smale index theorem for indefinite elliptic systems and bifurcation

DOI10.1016/j.jde.2014.11.010zbMath1310.35111arXiv1408.1419OpenAlexW2963975617MaRDI QIDQ2254054

Alessandro Portaluri, Nils Waterstraat

Publication date: 4 February 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.1419

zbMATH Keywords

bifurcationnonlinear elliptic systemFredholm quadratic formMorse-Smale index

Mathematics Subject Classification ID

Lagrangian submanifolds; Maslov index (53D12) Bifurcations in context of PDEs (35B32) Spectral flows (58J30) Semilinear elliptic equations (35J61) Boundary value problems for second-order elliptic systems (35J57)

Related Items (11)

Hadamard-type formulas via the Maslov form ⋮ The Morse and Maslov indices for Schrödinger operators ⋮ Bifurcation of critical points along gap-continuous families of subspaces ⋮ Index theorems for graph-parametrized optimal control problems ⋮ Corrigendum to: ``A Morse-Smale index theorem for indefinite elliptic systems and bifurcation ⋮ An index theory for asymptotic motions under singular potentials ⋮ Jacobi fields in optimal control: Morse and Maslov indices ⋮ The Maslov index and the spectra of second order elliptic operators ⋮ A \(K\)-theoretical invariant and bifurcation for homoclinics of Hamiltonian systems ⋮ The Morse and Maslov indices for multidimensional Schrödinger operators with matrix-valued potentials ⋮ Counting spectrum via the Maslov index for one dimensional $\theta -$periodic Schrödinger operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcation of critical points for continuous families of \(C^2\) functionals of Fredholm type
• Morse-Smale index theorems for elliptic boundary deformation problems
• Fredholm-Lagrangian-Grassmannian and the Maslov index
• Classes of linear operators. Vol. I
• Critical point theory and submanifold geometry
• On the Morse index in variational calculus
• The Maslov index: A functional analytical definition and the spectral flow formula
• Spectral flow and bifurcation of critical points of strongly-indefinite functionals. I: General theory
• The Maslov index for paths
• Conjugate points on spacelike geodesics or pseudo-self-adjoint Morse-Sturm-Liouville systems
• The Morse index theorem in Hilbert space
• The Morse index theorem in semi-Riemannian geometry
• The Maslov index, the spectral flow, and decompositions of manifolds
• On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem
• On bifurcation for semilinear elliptic Dirichlet problems on geodesic balls
• A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
• The homotopy type of the unitary group of Hilbert space
• Index theory for skew-adjoint Fredholm operators
• On coerciveness and semiboundedness of general boundary problems
• Spectral flow, crossing forms and homoclinics of Hamiltonian systems
• Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems
• Uniqueness in the Cauchy Problem for Partial Differential Equations
• The Spectral Flow and the Maslov Index
• A 𝐾-theoretic proof of the Morse index theorem in semi-Riemannian geometry
• Riemannian geometry.

This page was built for publication: A Morse-Smale index theorem for indefinite elliptic systems and bifurcation