| Citation: |
Suyun Wang, Yanhong Zhang, Ruyun Ma. THREE RADIAL POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS IN ${{\mathbb{R}}^{N}}$ $ ^* $[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 760-770. doi: 10.11948/20190145
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THREE RADIAL POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS IN ${{\mathbb{R}}^{N}}$ $ ^* $
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Abstract
This paper is concerned with the semilinear elliptic problem $\left\{ \begin{matrix} -\Delta u=\lambda h(|x|)f(u)\ \ \ \ \ \ \ \ \ \ \ \ \ \text{in}\ {{\mathbb{R}}^{N}}, \ u\left( x \right)>0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{in}\ {{\mathbb{R}}^{N}}, \ \ u\to 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rm{as}\left| x \right|\to \infty , \ \end{matrix} \right.$ 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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References
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Suyun Wang, Yanhong Zhang, Ruyun Ma. THREE RADIAL POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS IN ${{\mathbb{R}}^{N}}$ $ ^* $[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 760-770. doi: 10.11948/20190145
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