Miscellaneous properties of Sturm-Liouville problems in multiplicative calculus

Year 2023, Volume: 72 Issue: 4, 1141 - 1154, 29.12.2023

Güler Başak Öznur , Güher Gülçehre Özbey , Yelda Aygarküçükevcilioğlu , Rabia Aktaş

https://doi.org/10.31801/cfsuasmas.1272953

https://izlik.org/JA68RZ23TK

Abstract

The purpose of this paper is to investigate some properties of multiplicative regular and periodic Sturm-Liouville problems given in general form. We first introduce regular and periodic Sturm-Liouville (S-L) problems in multiplicative analysis by using some algebraic structures. Then, we discuss the main properties such as orthogonality of different eigenfunctions of the given problems. We show that the eigenfunctions corresponding to same eigenvalues are unique modulo a constant multiplicative factor and reality of the eigenvalues of multiplicative regular S-L problems. Finally, we present some examples to illustrate our main results.

Keywords

Multiplicative calculus , multiplicative derivative , multiplicative integral , Sturm-Liouville equation

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