| Title:
|
Solutions of Riemann–Weber type half-linear differential equation (English) |
| Author:
|
Došlý, Ondřej |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
49-61 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish an asymptotic formula for a pair of linearly independent solutions of the subcritical Riemann–Weber type half-linear differential equation. We also complement the results of the author and M. Ünal, Acta Math. Hungar. 120 (2008), 147–163, where the equation was considered in the critical case. (English) |
| Keyword:
|
Riemann–Weber half-linear differential equation |
| Keyword:
|
principal solution |
| Keyword:
|
modified Riccati equation |
| Keyword:
|
asymptotic formula |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 06738498 |
| idMR:
|
MR3636681 |
| DOI:
|
10.5817/AM2017-1-49 |
| . |
| Date available:
|
2017-03-23T10:06:41Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146075 |
| . |
| Reference:
|
[1] Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory of Second Order Linear, Half-Linear, Superlinear and Sublinear Differential Equations.Kluwer Acad. Publ., Dordrecht, Boston, London, 2002. MR 2091751 |
| Reference:
|
[2] Došlý, O., Elbert, Á.: Integral characterization of principal solution of half-linear differential equations.Studia Sci. Math. Hungar. 36 (2000), 455–469. MR 1798750 |
| Reference:
|
[3] Došlý, O., Fišnarová, S.: Half-linear oscillation criteria: Perturbation in term involving derivative.Nonlinear Anal. 73 (2010), 3756–3766. Zbl 1207.34041, MR 2728552, 10.1016/j.na.2010.07.049 |
| Reference:
|
[4] Došlý, O., Řehák, P.: Half-Linear Differential Equations.vol. 202, North-Holland Mathematical Studies, Elsevier, Amsterdam, 2005. Zbl 1090.34001, MR 2158903 |
| Reference:
|
[5] Došlý, O., Ünal, M.: Conditionally oscillatory half-linear differential equations.Acta Math. Hungar. 120 (2008), 147–163. Zbl 1199.34169, MR 2431365, 10.1007/s10474-007-7120-4 |
| Reference:
|
[6] Došlý, O., Yamaoka, N.: Oscillation constants for second-order ordinary differential equations related to elliptic equations with $p$-Laplacian.Nonlinear Anal. 113 (2015), 115–136. Zbl 1375.34051, MR 3281849 |
| Reference:
|
[7] Elbert, Á.: A half-linear second order differential equation.Qualitative theory of differential equations, Vol. I, II (Szeged, 1979), Colloq. Math. Soc. János Bolyai, 30, North-Holland, Amsterdam, New York, 1981, pp. 153–180. Zbl 0511.34006, MR 0680591 |
| Reference:
|
[8] Elbert, Á., Schneider, A.: Perturbations of the half-linear Euler differential equation.Results Math. 37 (2000), 56–83. Zbl 0958.34029, MR 1742294, 10.1007/BF03322512 |
| Reference:
|
[9] Hartman, P.: Ordinary Differential Equations.John Willey and Sons, Inc., New York, London, Sydney, 1974. MR 0171038 |
| Reference:
|
[10] Mirzov, J.D.: Asymptotic properties of solutions of systems of nonlinear nonautonomous ordinary differential equations.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 14 (2004). Zbl 1154.34300, MR 2144761 |
| . |
