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Positive solutions of a semilinear elliptic equation with singular nonlinearity |
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| Authors: | Hongxia Guo Ke Li |
| Affiliation: | a Department of Mathematics, Zhengzhou University, Zhengzhou 450052, PR China b Department of Mathematics, Henan Normal University, Xinxiang 453002, PR China c School of Mathematics and Statistics, Wuhan University 430072, PR China |
| Abstract: | This paper is devoted to the study of positive solutions of the semilinear elliptic equation Δu+K(|x|)u−p=0, x∈Rn with n?3 and p>0. Asymptotic behaviours of sky states and uniqueness of singular sky states are obtained via invariant manifold theory of dynamical systems. The Dirichlet problem in exterior domains is also studied. It is proved that this problem has infinitely many positive solutions with fast growth. |
| Keywords: | Semilinear elliptic equations Sky states Uniqueness |
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