Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Interval criteria for oscillation of second-order self-adjoint impulsive differential equations


Author: Jitsuro Sugie
Journal: Proc. Amer. Math. Soc. 148 (2020), 1095-1108
MSC (2010): Primary 34A37, 34C10, 34C29
DOI: https://doi.org/10.1090/proc/14797
Published electronically: December 6, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, oscillation theorems are given for second-order self-adjoint impulsive differential equations. The obtained results extend the well-known Kamenev-type and Philos-type oscillation theorems. A generalized Riccati transformation is used to prove these results. There are two advantages of using the generalized Riccati transformation rather than the standard Riccati transformation. One is that Kamenev-type and Philos-type oscillation theorems cannot be applied to conditionally oscillatory differential equations such as Euler's equations, but the obtained results can be applied even to such equations. The other advantage is the ability to prove that the impulsive differential equation may become oscillatory even if the total impulse is small. A specific example is included to demonstrate the merits of the results obtained.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 34A37, 34C10, 34C29

Retrieve articles in all journals with MSC (2010): 34A37, 34C10, 34C29


Additional Information

Jitsuro Sugie
Affiliation: Department of Mathematics, Shimane University, Matsue 690-8504, Japan
Email: jsugie@riko.shimane-u.ac.jp; jisugie@gmail.com

DOI: https://doi.org/10.1090/proc/14797
Keywords: Oscillation of solutions, impulse, generalized Riccati transformation, integral averaging technique
Received by editor(s): March 22, 2019
Published electronically: December 6, 2019
Additional Notes: This work was supported in part by JSPS KAKENHI Grants-in-Aid for Scientific Research (C)) Grant Number JP17K05327.
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society