Explicit connection coefficients and monodromy representations are constructed for the canonical solution matrices of a class of Okubo systems of ordinary differential equations as an application of the Katz operations.
In 2013, Tahara-Yamazawa showed multisummability of formal solutions of some linear partial differential equation under a certain condition on the Newton polygon. In this paper, we give an example such that a divergent formal power series solution is not multisummable when the condition on the Newton polygon by Tahara-Yamazawa does not hold.
We consider a sequence of blow-up solutions to the Liouville-Gel'fand problem with variable coefficients, and their linearized eigenvalue problems. We show the precise coincidence of the Morse indices of the solution and the critical point of the Hamiltonian of the singular limit. The results are natural extensions of those for constant coefficients.
In this paper we consider Schrödinger operators with potentials of order zero on asymptotically conic manifolds. We prove the existence and the completeness of the wave operators with a naturally defined free Hamiltonian.