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Three radial positive solutions for semilinear \\ elliptic problems in $\mathbb{R}^N
wang su yun,Zhang Yan hong,Ma ru yun
Keywords:Semilinear elliptic problem, radial positive solutions, eigenvalue, bifurcation, connected component.
Abstract:
      This paper is concerned with the semilinear elliptic problem $$ \left\{ \aligned &-\Delta u=\lambda h(|x|)f(u) \ \ \ \ \ \ \ \ \ \ \ \text{in}\ \mathbb{R}^N,\& u(x)>0\hskip 3cm \ \text{in}\ \mathbb{R}^N,\&u\to 0 \hskip 3cm \ \ \ \ \text{as}\ |x|\to \infty,\\endaligned \right. $$ 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.