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On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators. (English) Zbl 1319.35123
Summary: We consider a Sturm-Liouville boundary value problem in a bounded domain \(\mathcal D\) of \(\mathbb R^{n}\). By this is meant that the differential equation is given by a second order elliptic operator of divergent form in \(\mathcal D\) and the boundary conditions are of Robin type on \(\partial \mathcal D\). The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact selfadjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.

MSC:
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
47A55 Perturbation theory of linear operators
34B24 Sturm-Liouville theory
35J25 Boundary value problems for second-order elliptic equations
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