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Boundedness and asymptotic stability in a twospecies chemotaxiscompetition model with signaldependent sensitivity
Asymptotic behaviors of GreenSch 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 GreenSch 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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