TY  - JOUR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators
JF  - Journal of differential equations
N2  - We consider a Sturm-Liouville boundary value problem in a bounded domain D of R-n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on partial derivative 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. (C) 2013 Elsevier Inc. All rights reserved.
KW  - Sturm-Liouville problem
KW  - Discontinuous Robin condition
KW  - Root function
KW  - Lipschitz domain
KW  - Non-coercive problem
Y1  - 2013
U6  - https://doi.org/10.1016/j.jde.2013.07.029
SN  - 0022-0396
SN  - 1090-2732
VL  - 255
IS  - 10
SP  - 3305
EP  - 3337
PB  - Elsevier
CY  - San Diego
ER  -