THE RESOLVENT OF IMPULSIVE SINGULAR<i> q</i>-STURM-LIOUVILLE OPERATORS
HONAM MATHEMATICAL JOURNAL, vol.47, no.4, 2025 (ESCI)
- Publication Type: Article / Article
- Volume: 47 Issue: 4
- Publication Date: 2025
- Doi Number: 10.5831/hmj.2025.47.4.513
- Journal Name: HONAM MATHEMATICAL JOURNAL
- Journal Indexes: Emerging Sources Citation Index (ESCI)
- Azerbaijan State University of Economics (UNEC) Affiliated: Yes
Abstract
In this article, using the q-calculus, the resolvent of the qSturm-Lioville operator under impulsive boundary conditions is discussed. In this context, the historical development of the subject is discussed in the introduction. In the Preliminaries section, the basic concepts of qcalculus are given, i.e., q-derivative and q-integral definitions are given, and a Hilbert space for impulsive q-Sturm-Liouville problems is defined. In the main results section, Green's function corresponding to the impulsive q-Sturm-Liouville problem is established. With the help of Green's function, the resolvent operator for the impulsive q-Sturm-Liouville problem is defined. The compactness of the resolvent operator corresponding to the impulsive q-Sturm-Liouville problem is obtained by showing that this function is a Hilbert-Schmidth kernel. The spectral function corresponding to the impulsive q-Sturm-Liouville operator is generated. Using the spectral function, the integral representation of the resolvent operator of the impulsive q-Sturm-Liouville operator in the singular case is obtained.