Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms
We show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem $$ -Delta =k(x)g(u)+lambda |abla u|^q, quad u>0,; xin Omega,quad uig|_{partial{Omega}}=0, $$ where $Omega$ is a bounded domain with smooth boundary in $mathbb R^N$. We use the Karamata re...
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| Format: | Article |
| Language: | English |
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Texas State University
2006-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/93/abstr.html |
| _version_ | 1819266667912364032 |
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| author | Zhijun Zhang |
| author_facet | Zhijun Zhang |
| author_sort | Zhijun Zhang |
| collection | DOAJ |
| description | We show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem $$ -Delta =k(x)g(u)+lambda |abla u|^q, quad u>0,; xin Omega,quad uig|_{partial{Omega}}=0, $$ where $Omega$ is a bounded domain with smooth boundary in $mathbb R^N$. We use the Karamata regular varying theory, a perturbed argument, and constructing comparison functions. |
| first_indexed | 2024-12-23T21:04:55Z |
| format | Article |
| id | doaj.art-5f066a81fffd4b8c873bceee613ae60a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T21:04:55Z |
| publishDate | 2006-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-5f066a81fffd4b8c873bceee613ae60a2022-12-21T17:31:15ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-08-0120069318Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection termsZhijun ZhangWe show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem $$ -Delta =k(x)g(u)+lambda |abla u|^q, quad u>0,; xin Omega,quad uig|_{partial{Omega}}=0, $$ where $Omega$ is a bounded domain with smooth boundary in $mathbb R^N$. We use the Karamata regular varying theory, a perturbed argument, and constructing comparison functions.http://ejde.math.txstate.edu/Volumes/2006/93/abstr.htmlSemilinear elliptic equationsDirichlet problemsingularitynonlinear convection termsKaramata regular variation theoryunique solutionexact asymptotic behaviour. |
| spellingShingle | Zhijun Zhang Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms Electronic Journal of Differential Equations Semilinear elliptic equations Dirichlet problem singularity nonlinear convection terms Karamata regular variation theory unique solution exact asymptotic behaviour. |
| title | Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms |
| title_full | Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms |
| title_fullStr | Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms |
| title_full_unstemmed | Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms |
| title_short | Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms |
| title_sort | asymptotic behaviour of the solution for the singular lane emden fowler equation with nonlinear convection terms |
| topic | Semilinear elliptic equations Dirichlet problem singularity nonlinear convection terms Karamata regular variation theory unique solution exact asymptotic behaviour. |
| url | http://ejde.math.txstate.edu/Volumes/2006/93/abstr.html |
| work_keys_str_mv | AT zhijunzhang asymptoticbehaviourofthesolutionforthesingularlaneemdenfowlerequationwithnonlinearconvectionterms |