Electron. J. Differential Equations,
Vol. 2018 (2018), No. 02, pp. 115.
Global interval bifurcation and convex solutions for the
MongeAmpere equations
Wenguo Shen
Abstract:
In this article, we establish the global bifurcation result from the
trivial solutions axis or from infinity for the MongeAmpere equations
with nondifferentiable nonlinearity. By applying the above result,
we shall determine the interval of
,
in which there exist
radial solutions for the following MongeAmp\`ere equation
where
is the Hessian
matrix of u, where B is the unit open ball of
,
is a positive parameter.
is a radially symmetric weighted function and
on any subinterval of [0, 1] and the nonlinear term
but is not necessarily differentiable
at the origin and infinity.
We use global interval bifurcation techniques to prove our main results.
Submitted June 14, 2017. Published January 2, 2018.
Math Subject Classifications: 34B15, 34C10, 34C23.
Key Words: Global bifurcation; interval bifurcation; convex solutions;
MongeAmpere equations.
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Wenguo Shen
Department of Basic Courses
Lanzhou Institute of Technology
Lanzhou 730050, China
email: shenwg369@163.com

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