A Sturm comparison criterion for impulsive hyperbolic equations on a rectangular prism

Year 2025, Volume: 74 Issue: 1, 79 - 91

Abdullah Ozbekler , Kübra Uslu İşler

Abstract

In this paper, new Sturmian comparison results and oscillatory properties of linear impulsive hyperbolic equations are obtained on a rectangular prism under fixed moment of impulse effects. Besides the Kreith’s results [9, 10], this paper represents an extension of earlier findings obtained on the rectangular domain in the plane to the results obtained in rectangular prism in space.

Keywords

Impulsive hyperbolic equation, Sturm comparison, rectangular prism

References

• Bainov, D., Kamont, Z., Minchev, E., On first order impulsive partial differential inequalities, Appl. Math. Comput., 61 (2-3) (1994), 207–230. https://doi.org/10.1016/0096-3003(94)90048-5
• Bainov, D., Kamont, Z., Minchev, E., First-order impulsive partial differential inequalities, Internat. J. Theoret. Phys., 33(6) (1994), 1341–1358. https://doi.org/10.1007/BF00670798
• Bainov, D. D., Kamont, Z., Minchev, E., Comparison principles for impulsive hyperbolic equations of first order, J. Comput. Appl. Math., 60(3) (1995), 379–388. https://doi.org/10.1016/0377-0427(94)00046-4
• Bainov, D. D., Kamont, Z., Minchev, E., On the impulsive partial differential-functional inequalities of first order, Utilitas Math., 48 (1995), 107–128.
• Bainov, D., Simeonov, P., Oscillation Theory of Impulsive Differential Equations, International Publications, 1998.
• Cui, B. T., Liu, Y., Deng, F., Some oscillation problems for impulsive hyperbolic differential systems with several delays, Appl. Math. Comput., 146(2-3) (2003), 667–679. https://doi.org/10.1016/S0096-3003(02)00611-2
• Fu, X., Liu, X., Oscillation criteria for impulsive hyperbolic systems, Dynam. Contin. Discrete Impuls. Systems, 3(2) (1997), 225–244.
• Hernandez, E., Existence results for a partial second order functional differential equation with impulses, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 14(2) (2007), 229–250.
• Kreith, K., Sturmian theorems for hyperbolic equations, Proc. Amer. Math. Soc., 22 (1969), 277–281. https://doi.org/10.2307/2036969
• Kreith, K., Oscillation Theory, Springer-Verlag, New York, 1973. https://doi.org/10.1007/BFb0067537
• Lakshmikantham, V., Bainov, D. D., Simeonov, P. S., Theory of Impulsive Differential Equations, World Scientific Publishing Co., New Jersey, 1989. https://doi.org/10.1142/0906
• Luo, Q., Xiao, J., Deng, F., Oscillation of nonlinear partial functional differential equations with impulse, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, Intelligent and complex systems, (2003), 130–135.
• Luo, L. P., Zeng, Y. H., Luo, Z. G., Oscillation theorems for quasilinear hyperbolic systems with effect of impulse and delay, Acta Math. Appl. Sin., 37(5) (2014), 824–834.
• Minchev, E., Oscillation of solutions of impulsive nonlinear hyperbolic differential-difference equations, Math. Balkanica, 12(1-2) (1998), 215–224.
• Ning, C., Baodan, T., Yang, C., Jiqian, C., Some oscillation theorems of solutions for hyperbolic differential equations system with impulsive case, Far East J. Appl. Math., 62(2) (2012), 81–105.
• Özbekler, A., Uslu İşler, K., Sturm comparison criterion for impulsive hyperbolic equations, A Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 114(86) (2020), 1–10. https://doi.org/10.1007/s13398-020-00813-7
• Özbekler, A., Uslu İşler, K., Alzabut, J., Sturmian comparison theorem for hyperbolic equations on a rectangular prism, AIMS Mathematics, 9(20) (2024), 4805–4815. https://doi.org/10.3934/math.2024232
• Zhu, X., Li, Y., Lu, L., Oscillation criteria for impulsive hyperbolic equations of neutral type, Chinese Quart. J. Math., 21(2) (2006), 176–184.