A limit equation and bifurcation diagrams for semilinear elliptic equations with general supercritical growth
A limit equation and bifurcation diagrams for semilinear elliptic equations with general supercritical growth
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一般超临界增长半线性椭圆方程的极限方程和分岔图
DOI：
10.1016/j.jde.2017.10.034
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发表时间：
2018
影响因子：
2.4
通讯作者：
Yasuhito Miyamoto
中科院分区：
文献类型：
--
作者：
Yasuhito Miyamoto
我们研究半线性椭圆方程 Δ u+ f (u)= 0 在相当一般的 f 增长条件下的径向解。我们构造一个径向奇异解并研究奇异解与正则解之间的交集数。给出了椭圆狄利克雷问题在分岔问题中的应用。为此，我们使用广义相似变换从无穷远处的原始方程导出一定的极限方程。通过广义的 Cole–Hopf 变换，所有极限方程都可以简化为两种典型情况，即 Δ u+ u p= 0 和 Δ u+ e u= 0。
We study radial solutions of the semilinear elliptic equation Δ u+ f (u)= 0 under rather general growth conditions on f. We construct a radial singular solution and study the intersection number between the singular solution and a regular solution. An application to bifurcation problems of elliptic Dirichlet problems is given. To this end, we derive a certain limit equation from the original equation at infinity, using a generalized similarity transformation. Through a generalized Cole–Hopf transformation, all the limit equations can be reduced into two typical cases, ie, Δ u+ u p= 0 and Δ u+ e u= 0.