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13 gennaio |
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Tetsutaro Shibata (Hiroshima University) |
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Inverse and direct bifurcation problems for nonlinear elliptic
equations
Abstract: Recently, several investigators have been studying, especially in ODE field,
some nonlinear inverse and direct bifurcation problems in several frameworks. In this
talk, we introduce several typical inverse and direct bifurcation problems from a view
point of $L^q$-approach, variational approach, and recent results with respect to the
inverse and direct bifurcation problems.
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Shigeru Sakaguchi (Hiroshima University) |
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Liouville-type theorems characterizing hyperplanes
Abstract We consider a class W of Weingarten hypersurfaces in R^{N+1} with
N>=2, which contains an example related to stationary isothermic hypersurfaces.
Denote by C the class of continuous entire graphs x_{N+1} = f(x), x in R^N
over R^N such that the oscillation of f restricted on each unit ball in
R^N is bounded. Then, our main theorem is stated that, if S in C belongs to
W in the viscosity sense, then S must be a hyperplane. This theorem gives a
considerable improvement of the previous results of S. Sakaguchi ``A Liouville-type
theorem for some Weingarten hypersurfaces", Discrete and Continuous Dynamical Systems -
Series S 4 (2011), 887--895.
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