Lipschitz Stability of Inverse Nodal Problem for Energy-Dependent Sturm-Liouville Equation

Emrah Yilmaz

Lipschitz Stability of Inverse Nodal Problem for Energy-Dependent Sturm-Liouville Equation

Year 2015, Volume: 3 Issue: 3, 46 - 61, 26.06.2015

Abstract

In this study, we solve the reconstruction and some stability problems for diffusion operator using nodal set ofeigenfunctions. Moreover, we show that the space of all potential functions q is homeomorphic to the partition set of allasymptotically equivalent nodal sequences induced by an equivalence relation. To show this stability which is known Lipschitzstability, we have to construct two metric spaces and a mapΦdi fbetween these spaces. We find thatΦdi fis a homeomorphism whenthe corresponding metrics are magnified by the derivatives of q. Basically, this method is similar to [1] and [] which is given forSturm-Liouville and Hill operators, respectively and depends on the explicit asymptotic expansions of nodal points and nodal lengths

Keywords

Inverse Nodal Problem, Diffusion Equation, Lipschitz Stability

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