Linear perturbations of a nonoscillatory second-order dynamic equation

Abstract

We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and improve recently given conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and a dominant solution of the unperturbed equation. The presented results are time scales analogues of a 2002 paper on the differential equations case by Trench. The difference equations case has not been treated yet, but is contained in our study together with other cases of dynamic equations.

Keywords:

• recessive and dominant solution
• perturbation
• asymptotic behaviour
• dynamic equation
• time scale

Subject Classifications::

• 39A10

Acknowledgements

The authors would like to thank both referees for their exceptionally careful reading of the manuscript.

Notes

1. [email protected]

Additional information

Notes on contributors

Martin Bohner

1