Abstract
In mathematical physics (such as the one-dimensional time-independent Schrödinger equation), Sturm-Liouville problems occur very frequently. We construct, with a different perspective, a Sturm-Liouville problem in multiplicative calculus by some algebraic structures. Then, some asymptotic estimates for eigenfunctions of the multiplicative Sturm-Liouville problem are obtained by some techniques. Finally, some basic spectral properties of this multiplicative problem are examined in detail.
Highlights
In the 1960’s, Grossman and Katz [1, 2] constructed a comprehensive family of calculus that includes classical calculus as well an infinite subbranches of non-Newtonian calculus
We have constructed the multiplicative SL problem and obtained ∗eigenfunctions of that problem by using some techniques. This problem was investigated in terms of spectral theory in the multiplicative case
This study shows that multiplicative calculus methods can be applied to problems in spectral analysis and give solutions more effectively
Summary
In the 1960’s, Grossman and Katz [1, 2] constructed a comprehensive family of calculus that includes classical calculus as well an infinite subbranches of non-Newtonian calculus. Many events such as the levels of sound signals, the acidities of chemicals, and the magnitudes of earthquakes change exponentially For this reason, examining these problems in nature using multiplicative calculus offers great convenience and benefits. The problems encountered in the study of these physical properties can be expressed with multiplicative differential equations [3,4,5]. The analytical solution of a differential equation that is very difficult in classical calculus can be obtained more in multiplicative. In kindred areas of analysis and the SL theory that studies some properties such as asymptotic behavior of eigenvalues and eigenfunctions, these are a source of new problems and ideas [25] It is a very important equation used to explain many phenomena in nature. Multiplicative analysis techniques can be applied to different operators that have a significant impact on spectral theory
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