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II INTERNATIONAL SCIENTIFIC CONFERENCE OF YOUNG RESEARCHERS 

99 

 Qafqaz University                         

          18-19 April 2014, Baku, Azerbaijan 

The models which can be obtained investigating differential operators on graphs have both features of ordinary and partial 

differential operators. Many of the problems can be solved exactly. Such models have already been used by physicists; 

therefore this area is progressive and new. 

This problem can be considered as a generalization of the classical inverse spectral problem for the Schrodinger 

operator on the line. More complete investigations for spectral theory of differential operators was obtained for the Sturm -

Liouville equation. 

We will consider generalization of results obtained for direct and inverse  problems for Sturm- Liouville operator with 

complex, periodic potential of the type 

∑

 on star  graphs. 

Let’s, consider in the space 

0, ∞ ,

1,2,3  the operator  

,         

: 

0, ∞  

with 

 

 























1

1

,

]

[

n

nj

J

j

n

inx

nj

j

q

e

q

x

q

x

q

. 

We will introduce new spaces   

  and  

 by the way 

, ∞  

∑

, ∞ ,     

. 

and investigate direct and inverse problems on graphs for Sturm- Liouville problem  which is defined by following 

boundary and initial conditions 

 

 

    

0.