Global interval bifurcation and convex solutions for the Monge-Ampere equations
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Date
2018-01-02
Authors
Shen, Wenguo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Global bifurcation, Interval bifurcation, Convex solutions, Monge-Ampere equations
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.
Rights
Attribution 4.0 International