An expansion result for a Sturm-Liouville eigenvalue problem with impulse

Faydaoğlu Ş., Guseinov G. S.

TURKISH JOURNAL OF MATHEMATICS, vol.34, no.3, pp.355-366, 2010 (SCI-Expanded, Scopus, TRDizin) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.3906/mat-0809-34
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.355-366
  • Keywords: Green's function, Completely continuous operator, Impulse conditions, Eigenvalue, Eigenvector
  • Dokuz Eylül University Affiliated: Yes

Abstract

The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.