Index theorems for graph-parametrized optimal control problems
arXiv:2201.09719 · doi:10.1088/1361-6544/acc5d4
Abstract
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two Hessians related to two different graphs or two different sets of boundary conditions. Several applications such as the iteration formulas or lower bounds for the index are proved.
arXiv comment30 pages, 4 figures
References in corpus (11)
- Variational properties and orbital stability of standing waves for NLS equation on a star graph
- Functional Determinants in Quantum Field Theory
- Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
- Quadratic order conditions for bang-singular extremals
- A Morse complex for infinite dimensional manifolds - Part I
- A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds
- Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs
- An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity
- Heat Kernel Asymptotics, Path Integrals and Infinite-Dimensional Determinants
- Symplectic Geometry of Constrained Optimization
- Functional determinants for the second variation