Abstract
This paper concerns the oscillation of solutions to the second-order dynamic equation on a time scale which is unbounded above. No sign conditions are imposed on , , and . The function is assumed to satisfy and for . In addition, there is no need to assume certain restrictive conditions and also the both cases are considered. Our results will improve and extend results in (Baoguo et al. in Can. Math. Bull. 54:580-592, 2011; Bohner et al. in J. Math. Anal. Appl. 301:491-507, 2005; Hassan et al. in Comput. Math. Anal. 59:550-558, 2010; Hassan et al. in J. Differ. Equ. Appl. 17:505-523, 2011) and many known results on nonlinear oscillation. These results have significant importance to the study of oscillation criteria on discrete time scales such as , , , or and the space of harmonic numbers . Some examples illustrating the importance of our results are also included. MSC:34K11, 39A10, 39A99.
Highlights
The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD dissertation written under the direction of Bernd Aulbach
This paper concerns the oscillation of solutions to the second-order dynamic equation (r(t)x (t)) + p(t)x (t) + q(t)f (xσ (t)) = 0, on a time scale T which is unbounded above
1 Introduction The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD dissertation written under the direction of Bernd Aulbach
Summary
The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD dissertation written under the direction of Bernd Aulbach (see [ ]). This paper concerns the oscillation of solutions to the second-order dynamic equation (r(t)x (t)) + p(t)x (t) + q(t)f (xσ (t)) = 0, on a time scale T which is unbounded above. The function f ∈ C(R, R) is assumed to satisfy xf (x) > and f (x) > for x = .
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
