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 Volume 10, Number 2, 2020, Pages 760-770 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. PDF      Download reader