Singular left-definite Hamiltonian systems in the Sobolev space

Abstract

This paper is devoted to construct Weyl's theory for the singular left-definite even-order Hamiltonian systems in the corresponding Sobolev space. In particular, it is proved that there exist at least n-linearly independent solutions in the Sobolev space for the 2n-dimensional Hamiltonian system. (C) 2017 All rights reserved.