Article

Integral Equations and Operator Theory

, Volume 35, Issue 4, pp 485-506

First online:

A nonlocal boundary value problem for elliptic differential-operator equations and applications

  • Sasun YakubovAffiliated withDepartment of Mathematics and Computer Science, University of Haifa

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Abstract

In this paper we give, for the first time, an abstract interpretation of nonlocal boundary value problems for elliptic differential equations of the second order. We prove coerciveness and Fredholmness of nonlocal boundary value problems for the second order elliptic differential-operator equations. We apply then, in section 6, these results for investigation of nonlocal boundary value problems for the second order elliptic differential equations (one can find the references on the subject in the introduction and Chapter V in the book by A. L. Skubachevskii [27]). Abstract results obtained in this paper can be used for study of nonlocal boundary value problems for quasielliptic differential equations.

AMS subject classification

34L10