Inverse problems on star-type graphs: differential operators of different orders on different edges

Abstract

We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness. MSC:34A55, 34L05, 47E05

Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges

“…In this paper we study the general case of variable order differential equations on star-type graphs. The obtained results are natural generalizations of the well-known results on inverse problems for differential operators on an interval and on graphs and, in particular, generalizations of the results from [24]- [25]. Moreover, we consider general matching conditions in the interior vertex.…”

“…In [24]- [25] the inverse spectral problem is considered for a very particular case of variable order differential equations on star-type graphs when there are only two differential equations with different orders. In this paper we study the general case of variable order differential equations on star-type graphs.…”

“…License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use INVERSE PROBLEM FOR DIFFERENTIAL OPERATORS 105and matching conditions for variable order differential operators on graphs [24]. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.…”

“…and matching conditions for variable order differential operators on graphs [24]. Denote by Λ skμ = {λ lskμ } the eigenvalues of L skμ (counting with multiplicities).…”

Inverse problems for the differential operator on the graph with a cycle with different orders on different edges

“…Although for second-order differential operators the inverse spectral theory has been developed fairly completely, there are only a few works for higher-order operators [8]. In paper [9], V.A. Yurko started to study inverse problems for various order differential operators, i.e.…”