Half inverse problems for the impulsive quadratic pencil with the discontinouty coefficient
Citation
Rauf AMİROV , Sevim DURAK Department of Mathematics, Faculty of Sciences, Cumhuriyet University, Sivas, TurkeyAbstract
In this paper, we study the inverse spectral problem for the quadratic differential pencils with discontinuity
coefficient on [0, π] with separable boundary conditions and the impulsive conditions at the point x =
π
2
. We prove
that two potential functions on the interval [0, π] , and the parameters in the boundary and impulsive conditions can
be determined from a sequence of eigenvalues for two cases: (i) The potentials are given on
(
0,
π
4
(1 + α)
)
, (ii) The
potentials are given on
(π
4
(1 + α) , π
)
, where 0 < α < 1, respectively.