Coerciveness and isomorphism of discontinuous Sturm-Liouville problems with transmission conditions

Mustafa Kandemir; Murat Küçük

doi:10.54187/jnrs.1537253

EN

Coerciveness and isomorphism of discontinuous Sturm-Liouville problems with transmission conditions

Abstract

This study investigates a discontinuous Sturm-Liouville boundary value problem(BVP) on two intervals with functionals and transmission conditions in the direct sum ofSobolev spaces. Moreover, it presents the differential operator generated by the problem underinvestigation. The definition space of this operator is the direct sum of Sobolev spaces, andthe value space of the operator is the space obtained by adding the complex spaces where theboundary conditions are evaluated about the direct sum of Sobolev spaces. This paper establishesthe solvability of the problem and some important spectral properties of the operator, such asisomorphism, Fredholmness, and coerciveness concerning spectral parameters. In addition, theconclusion section discusses how different original problems can be produced.

Keywords

BVP , Functionaltransmission conditions , Isomorphism , Coerciveness , Solvability

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Mustafa Kandemir ^*
0000-0003-3212-8976
Türkiye

Murat Küçük
0009-0007-8655-4547
Türkiye

Publication Date

December 31, 2024

Submission Date

August 22, 2024

Acceptance Date

October 10, 2024

Published in Issue

Year 2024 Volume: 13 Number: 3

DOI

https://doi.org/10.54187/jnrs.1537253

IZ

https://izlik.org/JA74UC78WC

APA

Kandemir, M., & Küçük, M. (2024). Coerciveness and isomorphism of discontinuous Sturm-Liouville problems with transmission conditions. Journal of New Results in Science, 13(3), 175-185. https://doi.org/10.54187/jnrs.1537253

AMA

1.Kandemir M, Küçük M. Coerciveness and isomorphism of discontinuous Sturm-Liouville problems with transmission conditions. JNRS. 2024;13(3):175-185. doi:10.54187/jnrs.1537253

Chicago

Kandemir, Mustafa, and Murat Küçük. 2024. “Coerciveness and Isomorphism of Discontinuous Sturm-Liouville Problems With Transmission Conditions”. Journal of New Results in Science 13 (3): 175-85. https://doi.org/10.54187/jnrs.1537253.

EndNote

Kandemir M, Küçük M (December 1, 2024) Coerciveness and isomorphism of discontinuous Sturm-Liouville problems with transmission conditions. Journal of New Results in Science 13 3 175–185.

IEEE

[1]M. Kandemir and M. Küçük, “Coerciveness and isomorphism of discontinuous Sturm-Liouville problems with transmission conditions”, JNRS, vol. 13, no. 3, pp. 175–185, Dec. 2024, doi: 10.54187/jnrs.1537253.

ISNAD

Kandemir, Mustafa - Küçük, Murat. “Coerciveness and Isomorphism of Discontinuous Sturm-Liouville Problems With Transmission Conditions”. Journal of New Results in Science 13/3 (December 1, 2024): 175-185. https://doi.org/10.54187/jnrs.1537253.

JAMA

1.Kandemir M, Küçük M. Coerciveness and isomorphism of discontinuous Sturm-Liouville problems with transmission conditions. JNRS. 2024;13:175–185.

MLA

Kandemir, Mustafa, and Murat Küçük. “Coerciveness and Isomorphism of Discontinuous Sturm-Liouville Problems With Transmission Conditions”. Journal of New Results in Science, vol. 13, no. 3, Dec. 2024, pp. 175-8, doi:10.54187/jnrs.1537253.

Vancouver

1.Mustafa Kandemir, Murat Küçük. Coerciveness and isomorphism of discontinuous Sturm-Liouville problems with transmission conditions. JNRS. 2024 Dec. 1;13(3):175-8. doi:10.54187/jnrs.1537253