Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4625658 | Applied Mathematics and Computation | 2017 | 13 Pages |
Abstract
We establish asymptotic formulae for regularly varying solutions of the half-linear differential equation (r(t)|y′|α−1sgny′)′=p(t)|y|α−1sgny,where r, p are positive continuous functions on [a, ∞) and α ∈ (1, ∞). The results can be understood in several ways: Some open problems posed in the literature are solved. Results for linear differential equations are generalized; some of the observations are new even in the linear case. A refinement on information about behavior of solutions in standard asymptotic classes is provided. A precise description of regularly varying solutions which are known to exist is given. Regular variation of all positive solutions is proved.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Pavel Řehák,