Name
Title | ||
|---|---|---|
Asymptotic properties of Kneser solutions to nonlinear second order ODEs with regularly varying coefficients |
Abstract | ||
|---|---|---|
In this work, we investigate properties of a class of solutions to the second order ODE,
(p(t)u′(t))′+q(t)f(u(t))=0on the interval [a, ∞), a ≥ 0, where p and q are functions regularly varying at infinity, and f satisfies f(L0)=f(0)=f(L)=0, with L0 < 0 < L. Our aim is to describe the asymptotic behaviour of the non-oscillatory solutions satisfying one of the following conditions:
u(a)=u0∈(0,L),0≤u(t)≤L,t∈[a,∞),u(a)=u0∈(L0,0),L0≤u(t)≤0,t∈[a,∞).The existence of Kneser solutions on [a, ∞) is investigated and asymptotic properties of such solutions and their first derivatives are derived. The analytical findings are illustrated by numerical simulations using the collocation method. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.amc.2015.10.074 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Second order ordinary differential equations,Regular variation,Asymptotic properties,Non-oscillatory solutions,Kneser solutions | Mathematical optimization,Nonlinear system,Mathematical analysis,Infinity,Mathematics,Ode | Journal |
Volume | ISSN | Citations |
274 | 0096-3003 | 0 |
PageRank | References | Authors |
0.34 | 5 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jana Burkotová | 1 | 0 | 0.34 |
| Michael Hubner | 2 | 0 | 0.34 |
| Irena Rachunková | 3 | 0 | 0.34 |
| Ewa Weinmüller | 4 | 118 | 24.75 |