Asymptotic behavior of positive solutions of equation Δu + K(x) up = 0 in Rn
Asymptotic behavior of positive solutions of equation Δu + K(x) up = 0 in Rn
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DOI：
10.1016/0022-0396(92)90034-k
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发表时间：
1992-02
影响因子：
2.4
通讯作者：
Yi Li;Yi Li
中科院分区：
文献类型：
--
作者：
Yi Li;Yi Li
本文研究方程du+ f（x，u）= 0在W，n33（1）中的正解的渐近性态，特别是du+ K（~ x~）up= 0在iw”（2）中的正径向解的渐近性态，其中na 3且p> landK> 0在[W”中.方程（1）和（2）有许多数学和物理基础，如黎曼几何研究中著名的标量曲率方程，非线性薛定谔方程和Klein-Garden方程驻波的标量场方程，描述球状星团动力学的Matukuma方程等。(1)（1）的非平凡正解通常被称为基态。关于Eq. (1)（2）读者可以参考倪最近的一项调查。
In this paper we will study the asymptotic behavior of positive solutions of the following equation du+ f (x, u)= O in W, n33(1) and in particular, of positive radial solutions of du+ K (~ x~) up= o in iw”(2) withna3andp> landK> Oin [W”. Equations (1) and (2) have their roots from many mathematical and physical fields, eg, the well-known scalar curvature equation in the study of Riemannian geometry, the scalar field equation for the standing wave of nonlinear Schrodinger and Klein-Garden equations, the Matukuma equation describing the dynamics of globular cluster of stars, etc. And because of the variational structure of Eq.(1) the non-trivial positive solutions of (1) are usually referred to as the ground states. For a general overview on Eq.(1) and (2), readers may consult a recent survey [N2, and Ref. therein] by Ni.