Abstract
ОБ ОБРАТНОЙ ЗАДАЧЕ ДЛЯ ДИФФЕРЕНЦИАЛЬНЫХ ОПЕРАТОРОВ С ОТКЛОНЯЮЩИМСЯ АРГУМЕНТОМ
Highlights
We study the inverse spectral problem for Sturm – Liouville differential operators with a constant delay
Inverse spectral problems consist in constructing operators with given spectral characteristics
We study the inverse problem of constructing the potential q(x) and the coefficients Hj from the given two spectra of the boundary value problems Lj(q)
Summary
We study the inverse spectral problem for Sturm – Liouville differential operators with a constant delay. Given {μnj}n 0, j = 1, 2, construct q(x) and Hj. We note that in the case of large delay when a π/2, the characteristic functions of the problems Lj(q) depend on the potential q(x) linearly, i.e. the inverse problem becomes linear. We note that in the case of large delay when a π/2, the characteristic functions of the problems Lj(q) depend on the potential q(x) linearly, i.e. the inverse problem becomes linear This linear case was studied in [5, 7]. For a < π/2 the characteristic functions depend on the potential nonlinearly, i.e. the inverse problem becomes nonlinear This nonlinear case is seriously more difficult for investigating and for constructing the global solution of the inverse problem.
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