| Volume 10, Number 2, 2020, Pages 760-770 DOI：10.11948/20190145 |
| Three radial positive solutions for semilinear elliptic problems in $\mathbb{R}^N} |
| Suyun Wang,Yanhong Zhang,Ruyun Ma |
| Keywords:Semilinear elliptic problem, radial positive solutions, eigenvalue, bifurcation, connected component. |
| Abstract: |
| This paper is concerned with the semilinear elliptic problem
$$
\left\{
\begin{aligned}
&-\Delta u=\lambda h(|x|)f(u) \ \ \ \ \ \ \ \ \ \ \text{in}\ \mathbb{R}^N, \\~
& u(x)>0\hskip 3cm \ \text{in}\ \mathbb{R}^N, \\~
&u\to 0 \hskip 3cm \ \ \ \ \text{as}\ |x|\to \infty,
\end{aligned}
\right.
$$ where $\lambda$ is a real parameter and $h$ is a weight function which is positive. We show the existence of three radial positive solutions under suitable conditions on the nonlinearity. Proofs are mainly based on the bifurcation technique. |
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