On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators

Описание

Тип публикации: статья из журнала

Год издания: 2013

Идентификатор DOI: 10.1016/j.jde.2013.07.029

Ключевые слова: Sturm-Liouville problem, Discontinuous Robin condition, Root function, Lipschitz domain, Non-coercive problem

Аннотация: 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 deПоказать полностьюrivative 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.

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Издание

Журнал: JOURNAL OF DIFFERENTIAL EQUATIONS

Выпуск журнала: Vol. 255, Is. 10

Номера страниц: 3305-3337

ISSN журнала: 00220396

Место издания: SAN DIEGO

Издатель: ACADEMIC PRESS INC ELSEVIER SCIENCE

Авторы

  • Shlapunov Alexander (Siberian Fed Univ, Inst Math & Comp Sci, Krasnoyarsk 660041, Russia)
  • Tarkhanov Nikolai (Univ Potsdam, Inst Math, D-14469 Potsdam, Germany)

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