6 papers
Renormalized Oscillation Theory for Singular Linear Hamiltonian Systems
Peter Howard, Alim Sukhtayev
Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural…
A Sturm Liouville theorem for quadratic operator pencils
Alim Sukhtayev, Kevin Zumbrun
We establish a Sturm{Liouville theorem for quadratic operator pencils counting their unstable real roots, with applications to stability of waves. Such pencils arise, for example,…
Exponential dichotomies for elliptic PDE on radial domains
Margaret Beck, Graham Cox, Christopher Jones +2
It was recently shown by the authors that a semilinear elliptic equation can be represented as an infinite-dimensional dynamical system in terms of boundary data on a shrinking one…
A dynamical approach to semilinear elliptic equations
Margaret Beck, Graham Cox, Christopher Jones +2
A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in is given in terms of an infinite-dimensional dynamical system.…
The Maslov and Morse Indices for Sturm-Liouville Systems on the Half-Line
Peter Howard, Alim Sukhtayev
We show that for Sturm-Liouville Systems on the half-line , the Morse index can be expressed in terms of the Maslov index and an additional term associated with the bou…
The Maslov and Morse indices for Schrodinger operators on [0,1]
Peter Howard, Alim Sukhtayev
Assuming a symmetric potential and separated self-adjoint boundary conditions, we relate the Maslov and Morse indices for Schrödinger operators on . We find that the Morse…