### Abstract

This paper deals with the existence of positive radial solutions for the quasilinear system div(|∇_{ui}|^{p-2}∇_{ui} + λf^{i} (u_{1},...,u_{n}) = 0, |x| < 1, u_{i}(x) = 0, on |x| = 1, i = 1,...,n p > 1, λ > 0, x ∈ ℝ^{N}. The f^{i}, i = 1,..., n, are continuous and non-negative functions. Let u = (u_{1},...,u_{n}), ||u|| = Σ_{i=1}^{n} |u_{i}|, f_{0}^{i}= lim/||u||→0 f^{i}(u)/||u||^{p-1} i = 1,..., n, f = (f ^{1},..., f^{n}), f_{0} = Σ_{i=1} ^{n} f_{0}^{i}. We prove that the problem has a positive solution for sufficiently small λ > 0 if f_{0} = ∞. Our methods employ a fixed-point theorem in a cone.

Original language | English (US) |
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Pages (from-to) | 505-511 |

Number of pages | 7 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2006 |

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### Keywords

- Cone
- Elliptic system
- Existence
- Fixed-point theorem
- p-Laplacian

### ASJC Scopus subject areas

- Mathematics(all)