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THE BOUNDARY CONDITIONS DESCRIPTION OF TYPE I DOMAINS

  • MOHAMED EL-GEBEILY (a1) and DONAL O'REGAN (a2)
Abstract
Abstract

Type I domains are the domains of the self-adjoint operators determined by the weak formulation of formally self-adjoint differential expressions ℓ. This class of operators is defined by the requirement that the sesquilinear form q(u, v) obtained from ℓ by integration by parts agrees with the inner product 〈ℓu, v〉. A complete characterisation of the boundary conditions assumed by functions in these domains for second-order differential expressions is given in this paper. In the singular case, the boundary conditions are stated in terms of certain ‘boundary condition’ functions and in the regular case they are given in terms of classical function values.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

2.M. A. El-Gebeily , A. Boumenir and M. B. M. Elgindi , Existence and uniqueness of solutions of a class of two-point singular nonlinear boundary value problems, J. Comput. Appl. Math. 46 (1993), 345355.

3.M. A. El-Gebeily and K. M. Furati , Real self-adjoint Sturm–Liouville problems, Appl. Anal. 83 (4) (2004), 377387.

8.M. Marletta and A. Zettl , The Friedrichs extension of singular differential operators, J. Differ. Equ. 160 (2001), 404421.

11.D. O'Regan and M. El-Gebeily , Existence, upper and lower solutions and quasilinearization for singular differential equations, IMA J. Appl. Math. 73 (2008), 323344.

12.J. Weidmann , Spectral Theory of Ordinary Differential Operators, Lecture Notes in Mathematics, vol. 1258 (Springer, Heidelberg, Germany, 1987).

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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