Vyacheslav Pivovarchik RECOVERING A PART OF POTENTIAL BY PARTIAL INFORMATION ON SPECTRA OF BOUNDARY PROBLEMS
نویسنده
چکیده
Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm–Liouville equation on [0, a] with real potential q(x) ∈ L2(0, a), 2) a certain part of the spectrum of the Dirichlet problem for the same equation on [ 3 , a] and 3) the potential on [0, a 3 ]. The aim is to find the potential on [ 3 , a].
منابع مشابه
Ambarzumian’s Theorem for Trees
The classical Ambarzumian’s Theorem for Schrödinger operators −D2 + q on an interval, with Neumann conditions at the endpoints, says that if the spectrum of (−D2 + q) is the same as the spectrum of (−D2) then q = 0. This theorem is generalized to Schrödinger operators on metric trees with Neumann conditions at the boundary vertices.
متن کاملEigenvalue asymptotics for a star-graph damped vibrations problem
We consider a boundary value problem generated by Sturm-Liouville equations on the edges of a star-shaped graph. Thereby a continuity condition and a condition depending on the spectral parameter is imposed at the interior vertex, corresponding to the case of damping in the problem of small transversal vibrations of a star graph of smooth inhomogeneous strings. At the pendant vertices Dirichlet...
متن کاملAmbarzumyan–type Theorems on Star Graphs
The so-called Ambarzumyan theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator − d2 dx2 +q with an integrable real-valued potential q on [0,π] are {n2 : n 0} , then q = 0 for almost all x ∈ [0,π] . In this work, the classical Ambarzumyan theorem is extended to star graphs with Dirac operators on its edges. We prove that if the spectrum of Dirac operator on star graphs ...
متن کاملThe Study of Some Boundary Value Problems Including Fractional Partial Differential Equations with non-Local Boundary Conditions
In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations (FPDE) with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...
متن کاملOn the Convergence of Adaptive Non-Conforming Finite Element Methods
We formulate and analyze an adaptive non-conforming finite-element method for the solution of convex variational problems. The class of minimization problems we admit includes highly singular problems for which no Euler–Lagrange equation (or inequality) is available. As a consequence, our arguments only use the structure of the energy functional. We are nevertheless able to prove convergence of...
متن کامل