Positive Decreasing Solutions of Quasilinear Dynamic Equations
We consider a quasilinear dynamic equation reducing to a half-linear equation, an Emden-Fowler equation or a Sturm-Liouville equation under some conditions. Any nontrivial solution of the quasilinear dynamic equation is eventually monotone. In other words, it can be either positive decreasing (negative increasing) or positive increasing (negative decreasing). In particular, we investigate the asymptotic behavior of all positive decreasing solutions which are classified according to certain integral conditions. The approach is based on the Tychonov fixed point theorem
E. Akin, "Positive Decreasing Solutions of Quasilinear Dynamic Equations," Mathematical and Computer Modelling, Elsevier, Jan 2006.
The definitive version is available at https://doi.org/10.1016/j.mcm.2005.03.006
Mathematics and Statistics
University of Missouri Research Board
Keywords and Phrases
Sturm-Liouville equations; half-linear equations; measure chains; quasilinear equations; time scales
Article - Journal
© 2006 Elsevier, All rights reserved.