The oscillatory behavior of second order nonlinear elliptic equations
Some oscillation criteria are established for the nonlinear damped elliptic differential equation of second order $$ \sum_{i,\,j=1}^{N}D_i[\,a_{ij}(x)D_jy\,]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0, \tag{E} $$ which are different from most known ones in the sense that they are based on a new weighted...
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| Format: | Article |
| Language: | English |
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University of Szeged
2005-04-01
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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=216 |
| _version_ | 1797830793741991936 |
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| author | Zhiting Xu |
| author_facet | Zhiting Xu |
| author_sort | Zhiting Xu |
| collection | DOAJ |
| description | Some oscillation criteria are established for the nonlinear damped elliptic differential equation of second order
$$
\sum_{i,\,j=1}^{N}D_i[\,a_{ij}(x)D_jy\,]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0,
\tag{E}
$$
which are different from most known ones in the sense that they are based on a new weighted function $H(r,s,l)$ defined in the sequel. Both the cases when $D_ib_i(x)$ exists for all $i$ and when it does not exist for some $i$ are considered. |
| first_indexed | 2024-04-09T13:41:48Z |
| format | Article |
| id | doaj.art-94f6668292ce4e4eba92a1e9105e1a07 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:48Z |
| publishDate | 2005-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-94f6668292ce4e4eba92a1e9105e1a072023-05-09T07:52:57ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752005-04-012005811110.14232/ejqtde.2005.1.8216The oscillatory behavior of second order nonlinear elliptic equationsZhiting Xu0South China Normal University, Guangzhou, P. R. ChinaSome oscillation criteria are established for the nonlinear damped elliptic differential equation of second order $$ \sum_{i,\,j=1}^{N}D_i[\,a_{ij}(x)D_jy\,]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0, \tag{E} $$ which are different from most known ones in the sense that they are based on a new weighted function $H(r,s,l)$ defined in the sequel. Both the cases when $D_ib_i(x)$ exists for all $i$ and when it does not exist for some $i$ are considered.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=216 |
| spellingShingle | Zhiting Xu The oscillatory behavior of second order nonlinear elliptic equations Electronic Journal of Qualitative Theory of Differential Equations |
| title | The oscillatory behavior of second order nonlinear elliptic equations |
| title_full | The oscillatory behavior of second order nonlinear elliptic equations |
| title_fullStr | The oscillatory behavior of second order nonlinear elliptic equations |
| title_full_unstemmed | The oscillatory behavior of second order nonlinear elliptic equations |
| title_short | The oscillatory behavior of second order nonlinear elliptic equations |
| title_sort | oscillatory behavior of second order nonlinear elliptic equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=216 |
| work_keys_str_mv | AT zhitingxu theoscillatorybehaviorofsecondordernonlinearellipticequations AT zhitingxu oscillatorybehaviorofsecondordernonlinearellipticequations |