Global interval bifurcation and convex solutions for the Monge-Ampere equations
| dc.contributor.author | Shen, Wenguo | |
| dc.date.accessioned | 2021-12-15T16:26:14Z | |
| dc.date.available | 2021-12-15T16:26:14Z | |
| dc.date.issued | 2018-01-02 | |
| dc.description.abstract | In this article, we establish the global bifurcation result from the trivial solutions axis or from infinity for the Monge-Ampère equations with non-differentiable nonlinearity. By applying the above result, we shall determine the interval of γ, in which there exist radial solutions for the following Monge-Ampère equation det(D2u) = γα(x)F(-u), 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, γ is a positive parameter. α ∈ C(B-, [0, +∞)) is a radially symmetric weighted function and α(r) := α(|x|) ≢ 0 on any subinterval of [0, 1] and the nonlinear term F ∈ C(ℝ+) but is not necessarily differentiable at the origin and infinity. We use global interval bifurcation techniques to prove our main results. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 15 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Shen, W. (2018). Global interval bifurcation and convex solutions for the Monge-Ampere equations. <i>Electronic Journal of Differential Equations, 2018</i>(02), pp. 1-15. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15057 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Global bifurcation | |
| dc.subject | Interval bifurcation | |
| dc.subject | Convex solutions | |
| dc.subject | Monge-Ampere equations | |
| dc.title | Global interval bifurcation and convex solutions for the Monge-Ampere equations | en_US |
| dc.type | Article |