On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Annali di Matematica Pura ed Applicata. Series IV |
| MU Faculty or unit | |
| Citation | |
| Web | http://dx.doi.org/10.1007/s10231-017-0679-7 |
| Doi | http://dx.doi.org/10.1007/s10231-017-0679-7 |
| Field | General mathematics |
| Keywords | Linear Hamiltonian system; square integrable solution; Weyl solution; minimal principal solution at infinity; antiprincipal solution at infinity; limit point case; limit circle case |
| Attached files | |
| Description | New results in the Weyl-Titchmarsh theory for linear Hamiltonian differential systems are derived by using principal and antiprincipal solutions at infinity. In particular, a non-limit circle case criterion is established and a close connection between the Weyl solution and the minimal principal solution at infinity is shown in the limit point case. In addition, the square integrability of the columns of the minimal principal solution at infinity is investigated. All results are obtained without any controllability assumption. Several illustrative examples are also provided. |
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