Abstract
We establish a nonlinear extension of the Poincaré–Perron theorem for a second order half-linear differential equation. Conditions are established which guarantee that all nontrivial solutions y of the equation are such that a proper limit limt→∞y′(t)∕y(t) exists. In addition, we discuss establishing precise asymptotic formulae for these solutions. We employ theory of regular variation and thereby, as a by-product, we complete some results for asymptotics of differential equations considered in this framework. The results can serve for comparison purposes involving more general equations and are of importance also from the stability point of view.
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.
