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arXiv · 1912.11231

A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth

Yasuhito Miyamoto
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Abstract

We study radial solutions of the semilinear elliptic equation $\Delta u+f(u)=0$ 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, i.e., $\Delta u+u^p=0$ and $\Delta u+e^u=0$.

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Yasuhito Miyamoto. 2019-12-24. A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth. https://doi.org/10.1016/j.jde.2017.10.034

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