Asymptotic formulas for solutions of half-linear Euler-Weber equation
We establish improved asymptotic formulas for nonoscillatory solutions of the half-linear Euler-Weber type differential equation $$ (\Phi(x'))'+\left[\frac{\gamma_p}{t^p}+\frac{\mu_p}{t^p\log^2 t}\right]\Phi(x)=0, \quad \Phi(x):=|x|^{p-2}x,\quad p>1 $$ with critical coefficients $$\gamm...
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| Format: | Article |
| Language: | English |
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University of Szeged
2008-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=327 |
| _version_ | 1797830811481800704 |
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| author | Zuzana Pátíková |
| author_facet | Zuzana Pátíková |
| author_sort | Zuzana Pátíková |
| collection | DOAJ |
| description | We establish improved asymptotic formulas for nonoscillatory solutions of the half-linear Euler-Weber type differential equation
$$
(\Phi(x'))'+\left[\frac{\gamma_p}{t^p}+\frac{\mu_p}{t^p\log^2 t}\right]\Phi(x)=0, \quad \Phi(x):=|x|^{p-2}x,\quad p>1
$$
with critical coefficients
$$\gamma_p=\left(\frac{p-1}{p}\right)^p, \quad \mu_p= \frac{1}{2}\left(\frac{p-1}{p}\right)^{p-1},$$
where this equation is viewed as a perturbation of the half-linear Euler equation. |
| first_indexed | 2024-04-09T13:42:02Z |
| format | Article |
| id | doaj.art-ddfab8911df84bc18dc56b7950794aae |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:42:02Z |
| publishDate | 2008-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-ddfab8911df84bc18dc56b7950794aae2023-05-09T07:52:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752008-07-0120071511110.14232/ejqtde.2007.7.15327Asymptotic formulas for solutions of half-linear Euler-Weber equationZuzana Pátíková0Tomas Bata University in Zlín, Zlín, Czech RepublicWe establish improved asymptotic formulas for nonoscillatory solutions of the half-linear Euler-Weber type differential equation $$ (\Phi(x'))'+\left[\frac{\gamma_p}{t^p}+\frac{\mu_p}{t^p\log^2 t}\right]\Phi(x)=0, \quad \Phi(x):=|x|^{p-2}x,\quad p>1 $$ with critical coefficients $$\gamma_p=\left(\frac{p-1}{p}\right)^p, \quad \mu_p= \frac{1}{2}\left(\frac{p-1}{p}\right)^{p-1},$$ where this equation is viewed as a perturbation of the half-linear Euler equation.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=327 |
| spellingShingle | Zuzana Pátíková Asymptotic formulas for solutions of half-linear Euler-Weber equation Electronic Journal of Qualitative Theory of Differential Equations |
| title | Asymptotic formulas for solutions of half-linear Euler-Weber equation |
| title_full | Asymptotic formulas for solutions of half-linear Euler-Weber equation |
| title_fullStr | Asymptotic formulas for solutions of half-linear Euler-Weber equation |
| title_full_unstemmed | Asymptotic formulas for solutions of half-linear Euler-Weber equation |
| title_short | Asymptotic formulas for solutions of half-linear Euler-Weber equation |
| title_sort | asymptotic formulas for solutions of half linear euler weber equation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=327 |
| work_keys_str_mv | AT zuzanapatikova asymptoticformulasforsolutionsofhalflineareulerweberequation |