Sturmian comparison theorem for hyperbolic equations on a rectangular prism

Abdullah Özbekler; Kübra Uslu İşler; Jehad Alzabut; Abdullah Özbekler; Kübra Uslu İşler; Jehad Alzabut

doi:10.3934/math.2024232

AIMS Mathematics

2024, Volume 9, Issue 2: 4805-4815. doi: 10.3934/math.2024232

Previous Article Next Article

Research article Special Issues

Sturmian comparison theorem for hyperbolic equations on a rectangular prism

1.
Department of Industrial Engineering, OSTİM Technical University, Ankara, Türkiye
2.
Department of Mathematics, Bolu Abant İzzet Baysal University, Bolu, Türkiye
3.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Received: 03 September 2023 Revised: 22 December 2023 Accepted: 05 January 2024 Published: 22 January 2024
MSC : 34C10, 35L10, 35L20, 35L70

In this paper, new Sturmian comparison results were obtained for linear and nonlinear hyperbolic equations on a rectangular prism. The results obtained for linear equations extended those given by Kreith [Sturmian theorems on hyperbolic equations, Proc. Amer. Math. Soc., 22 (1969), 277-281] in which the Sturmian comparison theorem for linear equations was obtained on a rectangular region in the plane. For the purpose of verification, an application was described using an eigenvalue problem.
- hyperbolic equation,
- Sturm comparison,
- rectangular prism,
- oscillation,
- eigenvalue problem,
- hyperrectangle
Citation: Abdullah Özbekler, Kübra Uslu İşler, Jehad Alzabut. Sturmian comparison theorem for hyperbolic equations on a rectangular prism[J]. AIMS Mathematics, 2024, 9(2): 4805-4815. doi: 10.3934/math.2024232

Related Papers:

Abstract

In this paper, new Sturmian comparison results were obtained for linear and nonlinear hyperbolic equations on a rectangular prism. The results obtained for linear equations extended those given by Kreith [Sturmian theorems on hyperbolic equations, Proc. Amer. Math. Soc., 22 (1969), 277-281] in which the Sturmian comparison theorem for linear equations was obtained on a rectangular region in the plane. For the purpose of verification, an application was described using an eigenvalue problem.

References

[1]	Z. Kayar, Sturm-Picone type theorems for second order nonlinear impulsive differential equations, AIP Conf. Proc., 1863 (2017), 140007. https://doi.org/10.1063/1.4992314 doi: 10.1063/1.4992314
[2]	O. Moaaz, G. E. Chatzarakis, T. Abdeljawad, C. Cesarano, A. Nabih, Amended oscillation criteria for second-order neutral differential equations with damping term, Adv. Differ. Equ., 2020 (2020), 1–12. https://doi.org/10.1186/s13662-020-03013-0 doi: 10.1186/s13662-020-03013-0
[3]	H. Ahmad, T. A. Khan, P. S. Stanimirovic, W. Shatanawi, T. Botmart, New approach on conventional solutions to nonlinear partial differential equations describing physical phenomena, Results Phys., 41 (2022), 105936. https://doi.org/10.1016/j.rinp.2022.105936 doi: 10.1016/j.rinp.2022.105936
[4]	A. Palanisamy, J. Alzabut, V. Muthulakshmi, S. S. Santra, K. Nonlaopon, Oscillation results for a fractional partial differential system with damping and forcing terms, AIMS Math., 8 (2023), 4261–4279. https://doi.org/10.3934/math.2023212 doi: 10.3934/math.2023212
[5]	P. Hartman, A. Wintner, On a comparison theorem for self-adjoint partial differential equations of elliptic type, Proc. Amer. Math. Soc., 6 (1955), 862–865.
[6]	S. Shimoda, Comparison theorems and various related principles in the theory of second order partial differential equations of elliptic type, Sūgaku, 9 (1957), 153–166.
[7]	T. Kusano, N. Yoshida, Comparison and nonoscillation theorems for fourth order elliptic systems, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend., 59 (1975), 328–337.
[8]	N. Yoshida, Nonoscillation and comparison theorems for a class of higher order elliptic systems, Japan. J. Math., 2 (1976), 419–434. https://doi.org/10.4099/math1924.2.419 doi: 10.4099/math1924.2.419
[9]	T. Kusano, J. Jaroš, N. Yoshida, A Picone-type identity and Sturmian comparison and oscillation theorems for a class of half-linear partial differential equations of second order, Nonlinear Anal., 40 (2000), 381–395. https://doi.org/10.1016/S0362-546X(00)85023-3 doi: 10.1016/S0362-546X(00)85023-3
[10]	N. Yoshida, Sturmian comparison and oscillation theorems for a class of half-linear elliptic equations, Nonlinear Anal., 71 (2009), e1354–e1359. https://doi.org/10.1016/j.na.2009.01.141 doi: 10.1016/j.na.2009.01.141
[11]	N. Yoshida, Sturmian comparison and oscillation theorems for quasilinear elliptic equations with mixed nonlinearities via Picone-type inequality, Toyama Math. J., 33 (2010), 21–41.
[12]	N. Yoshida, Picone identities for half-linear elliptic operators with $p(x)$-Laplacians and applications to Sturmian comparison theory, Nonlinear Anal., 74 (2011), 5631–5642. https://doi.org/10.1016/j.na.2011.05.048 doi: 10.1016/j.na.2011.05.048
[13]	N. Yoshida, Picone-type inequality and Sturmian comparison theorems for quasilinear elliptic operators with $p(x)$-Laplacians, Electron. J. Differ. Equ., 2012 (2012), 1–9.
[14]	J. Jaroš, Picone-type identity and comparison results for a class of partial differential equations of order $4m$, Opuscula Math., 33 (2013), 701–711. https://doi.org/10.7494/OpMath.2013.33.4.701 doi: 10.7494/OpMath.2013.33.4.701
[15]	J. B. Diaz, J. R. McLaughlin, Sturm comparison theorems for ordinary and partial differential equations, Bull. Amer. Math. Soc., 75 (1969), 335–339.
[16]	J. B. Diaz, J. R. McLaughlin, Sturm separation and comparison theorems for ordinary and partial differential equations, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. I, 9 (1969), 135–194.
[17]	N. Yoshida, Oscillation theory of partial differential equations, World Scientific, 2008.
[18]	K. Kreith, Sturmian theorems for hyperbolic equations, Proc. Amer. Math. Soc., 22 (1969), 277–281.
[19]	K. Kreith, Oscillation theory, Springer, 1973. https://doi.org/10.1007/BFb0067537
[20]	K. Kreith, Oscillation theorems for elliptic equations, Proc. Amer. Math. Soc., 15 (1964), 341–344.

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)