Journal of the Ramanujan Mathematical Society

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Direct and Inverse Spectral Assignment for the Operator Sturm-Liuoville type with Linear Delay


Affiliations
1 Polytechnic Faculty of the University of Zenica, Zenica, Bosnia and Herzegovina
2 University of East Sarajevo, Bosnia and Herzegovina
3 University of Zenica, Zenica, Bosnia and Herzegovina
4 University of Sarajevo, Sarajevo, Bosnia and Herzegovina
     

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In this paper, we constructed the solution of the spectral boundary problem on [0, π] with zero initial function and separated boundary conditions. In this work, characteristic function is constructed and asymptotics of its large zeroes and eigenvalues asymptotics of the operator are found. In the second part of this paper, it is assumed that two sets of eigenvalues are given when h = 0. Under certain conditions of the linear delay, the parameters of operators are found. It means that we solved the inverse spectral problem using a Fourier’s series method.
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  • Direct and Inverse Spectral Assignment for the Operator Sturm-Liuoville type with Linear Delay

Abstract Views: 274  |  PDF Views: 1

Authors

Ismet Kalco
Polytechnic Faculty of the University of Zenica, Zenica, Bosnia and Herzegovina
Milenko Pikula
University of East Sarajevo, Bosnia and Herzegovina
Dzevad Burgic
University of Zenica, Zenica, Bosnia and Herzegovina
Fatih Destovic
University of Sarajevo, Sarajevo, Bosnia and Herzegovina

Abstract


In this paper, we constructed the solution of the spectral boundary problem on [0, π] with zero initial function and separated boundary conditions. In this work, characteristic function is constructed and asymptotics of its large zeroes and eigenvalues asymptotics of the operator are found. In the second part of this paper, it is assumed that two sets of eigenvalues are given when h = 0. Under certain conditions of the linear delay, the parameters of operators are found. It means that we solved the inverse spectral problem using a Fourier’s series method.