18 citations · 46 across the 17 of their papers we have counts for
21 papers
Renormalized oscillation theory for singular linear Hamiltonian pencils
Peter Howard, Alim Sukhtayev
For many applications, critical information about system dynamics is encoded in associated eigenvalue problems that can be posed as linear Hamiltonian systems with suitable boundar…
Splitting Quantum Graphs
Nathaniel Smith, Alim Sukhtayev
We derive a counting formula for the eigenvalues of Schrödinger operators with self-adjoint boundary conditions on quantum star graphs. More specifically, we develop techniques usi…
Fredholm determinants, Evans functions and Maslov indices for partial differential equations
Graham Cox, Yuri Latushkin, Alim Sukhtayev
The Evans function is a well known tool for locating spectra of differential operators in one spatial dimension. In this paper we construct a multidimensional analogue as the modif…
Spectral decomposition and decay to grossly determined solutions for a simplified BGK model
Alim Sukhtayev, Kevin Zumbrun
Extending work of Carty, we show that solutions of a simplified 1D BGK model decay exponentially in to a subclass of the class of grossly determined solutions as define…
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,…