Positive solutions and global bifurcation of strongly coupled elliptic systems
In this article, we study the existence of positive solutions for the coupled elliptic system egin{gather*} -Delta u= lambda (f(u, v)+ h_{1}(x) ) quad ext{in }Omega, \ -Delta v= lambda (g(u, v)+ h_{2}(x))quad ext{in }Omega, \ u =v=0 quad ext{on }partial Omega, end{gather*} under certain condi...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-03-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/82/abstr.html |
| _version_ | 1818472865134018560 |
|---|---|
| author | Jagmohan Tyagi |
| author_facet | Jagmohan Tyagi |
| author_sort | Jagmohan Tyagi |
| collection | DOAJ |
| description | In this article, we study the existence of positive solutions for the coupled elliptic system egin{gather*} -Delta u= lambda (f(u, v)+ h_{1}(x) ) quad ext{in }Omega, \ -Delta v= lambda (g(u, v)+ h_{2}(x))quad ext{in }Omega, \ u =v=0 quad ext{on }partial Omega, end{gather*} under certain conditions on $f,g$ and allowing $h_1, h_2$ to be singular. We also consider the system egin{gather*} -Delta u= lambda ( a(x) u + b(x)v+ f_{1}(v)+ f_{2}(u) ) quad ext{in }Ome ga, \ -Delta v= lambda ( b(x)u+ c(x)v+ g_{1}(u)+ g_{2}(v) )quad ext{in }Omega , \ u =v=0 quad ext{on }partial Omega, end{gather*} and prove a Rabinowitz global bifurcation type theorem to this system. |
| first_indexed | 2024-04-14T04:13:18Z |
| format | Article |
| id | doaj.art-b755169c2edb40b08b63f912ef318ad1 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-14T04:13:18Z |
| publishDate | 2013-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-b755169c2edb40b08b63f912ef318ad12022-12-22T02:13:01ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-03-01201382,111Positive solutions and global bifurcation of strongly coupled elliptic systemsJagmohan TyagiIn this article, we study the existence of positive solutions for the coupled elliptic system egin{gather*} -Delta u= lambda (f(u, v)+ h_{1}(x) ) quad ext{in }Omega, \ -Delta v= lambda (g(u, v)+ h_{2}(x))quad ext{in }Omega, \ u =v=0 quad ext{on }partial Omega, end{gather*} under certain conditions on $f,g$ and allowing $h_1, h_2$ to be singular. We also consider the system egin{gather*} -Delta u= lambda ( a(x) u + b(x)v+ f_{1}(v)+ f_{2}(u) ) quad ext{in }Ome ga, \ -Delta v= lambda ( b(x)u+ c(x)v+ g_{1}(u)+ g_{2}(v) )quad ext{in }Omega , \ u =v=0 quad ext{on }partial Omega, end{gather*} and prove a Rabinowitz global bifurcation type theorem to this system.http://ejde.math.txstate.edu/Volumes/2013/82/abstr.htmlElliptic systembifurcationpositive solutions |
| spellingShingle | Jagmohan Tyagi Positive solutions and global bifurcation of strongly coupled elliptic systems Electronic Journal of Differential Equations Elliptic system bifurcation positive solutions |
| title | Positive solutions and global bifurcation of strongly coupled elliptic systems |
| title_full | Positive solutions and global bifurcation of strongly coupled elliptic systems |
| title_fullStr | Positive solutions and global bifurcation of strongly coupled elliptic systems |
| title_full_unstemmed | Positive solutions and global bifurcation of strongly coupled elliptic systems |
| title_short | Positive solutions and global bifurcation of strongly coupled elliptic systems |
| title_sort | positive solutions and global bifurcation of strongly coupled elliptic systems |
| topic | Elliptic system bifurcation positive solutions |
| url | http://ejde.math.txstate.edu/Volumes/2013/82/abstr.html |
| work_keys_str_mv | AT jagmohantyagi positivesolutionsandglobalbifurcationofstronglycoupledellipticsystems |