### Abstract

The existence of positive solutions is discussed for some nonlinear elliptic equations involving the nonlinear terms with the growth order of super-critical exponents in exterior domains of balls such as -Δu = u ^{β} in Ω, ((N + 2)/(N - 2) < β), u = 0 on ∂B, with Ω = ℝ^{N}\Ω̄ where Ω_{0} is the open ball. To recover the compactness of the embedding L ^{β+1}(Ω) ⊂ H_{0}
^{1}(Ω, we work in the class of radially symmetric functions and introduce a new transformation, which reduces our problems to some nonlinear elliptic equations in annuli but with coefficients which have some singularity on the boundary. The difficulty caused by the singularity on the boundary will be managed by the arguments developed in our previous work.

Original language | English |
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Pages (from-to) | 323-333 |

Number of pages | 11 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 19 |

Issue number | 2 |

Publication status | Published - 2007 Oct |

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### Keywords

- Exterior domain
- P-Laplacian
- Supercritical exponent

### ASJC Scopus subject areas

- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis

### Cite this

*Discrete and Continuous Dynamical Systems*,

*19*(2), 323-333.