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¯,...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/9269458 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2314-8896 2314-8888 |