【摘 要】
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In this talk, we introduce a method of the potential analysis to study the properties of the positive solutions of a γ-Laplace system in Rn-div(|▽u|γ-2▽
【出 处】
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2011年度长江三角洲偏微分方程学术研讨会暨长江三角洲偏微分方程博士生论坛
论文部分内容阅读
In this talk, we introduce a method of the potential analysis to study the properties of the positive solutions of a γ-Laplace system in Rn-div(|▽u|γ-2▽u) =u pvq,-div(|▽v|γ-2▽v) =vpuq.Here 1 < γ ≤ 2, p,q > 0 satisfy the critical condition p+q =γ *-1.First, the positive solutions u and v satisfy an integral system involving the Wolff potentials.We then use the method of regularity lifting to obtain an optimal integrability for this Wolff type integral system.Different from the case of γ =2, it is more difficult to handle the asymptotics since u and v have not radial structures.We overcome this difficulty by a new method and obtain the decay rates of u and v as |x| → ∞.We believe that this new method is appropriate to deal with the asymptotics of other decaying solutions without the radial structures.
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