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Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity
Asymptotic behaviors of Green-Sch potentials at infinity and its applications
School of of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, China |
The first aim in this paper is to deal with asymptotic behaviors of Green-Sch potentials in a cylinder. As an application we prove the integral representation of nonnegative weak solutions of the stationary Schrödinger equation in a cylinder. Next we give asymptotic behaviors of them outside an exceptional set. Finally we obtain a quantitative property of rarefied sets with respect to the stationary Schrödinger operator at $+\infty$ in a cylinder. Meanwhile we show that the reverse of this property is not true.
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