Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators
We study the maximum principle and existence of positive solutions for the nonlinear system egin{gather*} -Delta _{p,_{P}}u=a(x)|u|^{p-2}u+b(x)|u|^{alpha }|v|^{eta }v+f quad ext{in } Omega , \ -Delta _{Q,q}v=c(x)|u|^{alpha }|v|^{eta }u+d(x)|v|^{q-2}v+g quad ext{in } Omega , \ u=v=0 quad ext{on }p...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2007-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/66/abstr.html |
| _version_ | 1818023080936603648 |
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| author | Salah A. Khafagy Hassan M. Serag |
| author_facet | Salah A. Khafagy Hassan M. Serag |
| author_sort | Salah A. Khafagy |
| collection | DOAJ |
| description | We study the maximum principle and existence of positive solutions for the nonlinear system egin{gather*} -Delta _{p,_{P}}u=a(x)|u|^{p-2}u+b(x)|u|^{alpha }|v|^{eta }v+f quad ext{in } Omega , \ -Delta _{Q,q}v=c(x)|u|^{alpha }|v|^{eta }u+d(x)|v|^{q-2}v+g quad ext{in } Omega , \ u=v=0 quad ext{on }partial Omega , end{gather*} where the degenerate p-Laplacian defined as $Delta _{p,_{P}}u=mathop{m div}[P(x)| abla u|^{p-2} abla u]$. We give necessary and sufficient conditions for having the maximum principle for this system and then we prove the existence of positive solutions for the same system by using an approximation method. |
| first_indexed | 2024-12-10T03:38:38Z |
| format | Article |
| id | doaj.art-abcb5444470a4e1a972beb6b53706af6 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T03:38:38Z |
| publishDate | 2007-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-abcb5444470a4e1a972beb6b53706af62022-12-22T02:03:39ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-04-01200766114Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operatorsSalah A. KhafagyHassan M. SeragWe study the maximum principle and existence of positive solutions for the nonlinear system egin{gather*} -Delta _{p,_{P}}u=a(x)|u|^{p-2}u+b(x)|u|^{alpha }|v|^{eta }v+f quad ext{in } Omega , \ -Delta _{Q,q}v=c(x)|u|^{alpha }|v|^{eta }u+d(x)|v|^{q-2}v+g quad ext{in } Omega , \ u=v=0 quad ext{on }partial Omega , end{gather*} where the degenerate p-Laplacian defined as $Delta _{p,_{P}}u=mathop{m div}[P(x)| abla u|^{p-2} abla u]$. We give necessary and sufficient conditions for having the maximum principle for this system and then we prove the existence of positive solutions for the same system by using an approximation method.http://ejde.math.txstate.edu/Volumes/2007/66/abstr.htmlMaximum principleexistence of positive solutionnonlinear elliptic systemdegenerated p-Laplacian. |
| spellingShingle | Salah A. Khafagy Hassan M. Serag Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators Electronic Journal of Differential Equations Maximum principle existence of positive solution nonlinear elliptic system degenerated p-Laplacian. |
| title | Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators |
| title_full | Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators |
| title_fullStr | Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators |
| title_full_unstemmed | Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators |
| title_short | Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators |
| title_sort | maximum principle and existence of positive solutions for nonlinear systems involving degenerate p laplacian operators |
| topic | Maximum principle existence of positive solution nonlinear elliptic system degenerated p-Laplacian. |
| url | http://ejde.math.txstate.edu/Volumes/2007/66/abstr.html |
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