Fourth order differential operators with distributional potentials

Ugurlu E., Bairamov E.

TURKISH JOURNAL OF MATHEMATICS, vol.44, no.3, pp.825-856, 2020 (SCI-Expanded, Scopus, TRDizin) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1706-34
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.825-856
  • Keywords: Distributional potentials, deficiency indices, extension theory, direct sum operator, STURM-LIOUVILLE OPERATORS, 1ST-ORDER, EXTENSIONS
  • Ankara University Affiliated: Yes

Abstract

In this paper, regular and singular fourth order differential operators with distributional potentials are investigated. In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied. These symmetric operators are considered as acting on the single and direct sum Hilbert spaces. The latter one consists of three Hilbert spaces such that a squarely integrable space and two spaces of complex numbers. Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single and direct sum Hilbert spaces.