Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications
We shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u)=λm(x)-uN+m(x)f1(x,-u,-u′,λ)+f2(x,-u,-u′,λ), in B, u(x)=0, on ∂B, where D2u=(∂2u/∂xi∂xj) is the Hessian matrix of u, where B is the unit open ball of RN, m∈C(B¯,...
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| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/9269458 |
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| author | Wenguo Shen |
| author_facet | Wenguo Shen |
| author_sort | Wenguo Shen |
| collection | DOAJ |
| description | We shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u)=λm(x)-uN+m(x)f1(x,-u,-u′,λ)+f2(x,-u,-u′,λ), in B, u(x)=0, on ∂B, where D2u=(∂2u/∂xi∂xj) is the Hessian matrix of u, where B is the unit open ball of RN, m∈C(B¯,[0,+∞)) is a radially symmetric weighted function and m(r):=m(x)≢0 on any subinterval of [0,1], λ is a positive parameter, and the nonlinear term f1,f2∈C(B¯×R+3,R+), but f1 is not necessarily differentiable at the origin and infinity with respect to u, where R+=[0,+∞). Some applications are given to the Monge-Ampère equations and we use global bifurcation techniques to prove our main results. |
| format | Article |
| id | doaj-art-5ba4e6592d564d11a61296b5c5bf2ffd |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-5ba4e6592d564d11a61296b5c5bf2ffd2025-02-03T05:58:20ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/92694589269458Global Bifurcation from Intervals for the Monge-Ampère Equations and Its ApplicationsWenguo Shen0Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, ChinaWe shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u)=λm(x)-uN+m(x)f1(x,-u,-u′,λ)+f2(x,-u,-u′,λ), in B, u(x)=0, on ∂B, where D2u=(∂2u/∂xi∂xj) is the Hessian matrix of u, where B is the unit open ball of RN, m∈C(B¯,[0,+∞)) is a radially symmetric weighted function and m(r):=m(x)≢0 on any subinterval of [0,1], λ is a positive parameter, and the nonlinear term f1,f2∈C(B¯×R+3,R+), but f1 is not necessarily differentiable at the origin and infinity with respect to u, where R+=[0,+∞). Some applications are given to the Monge-Ampère equations and we use global bifurcation techniques to prove our main results.http://dx.doi.org/10.1155/2018/9269458 |
| spellingShingle | Wenguo Shen Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications Journal of Function Spaces |
| title | Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications |
| title_full | Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications |
| title_fullStr | Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications |
| title_full_unstemmed | Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications |
| title_short | Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications |
| title_sort | global bifurcation from intervals for the monge ampere equations and its applications |
| url | http://dx.doi.org/10.1155/2018/9269458 |
| work_keys_str_mv | AT wenguoshen globalbifurcationfromintervalsforthemongeampereequationsanditsapplications |