## Abstract

We consider the existence of positive solutions of the following semilinear elliptic problem in ℝ^{N}: (Formula Presented) where 1 < p < N + 2/N - 2 (N ≥ 3), 1 < p < ∞ (N = 1, 2), a(x) ∈ C(ℝ^{N}), f(x) ∈ H^{-1} (ℝ^{N}) and f(x) ≥ 0. Under the conditions: 1° a(x) ∈ (0, 1) for all x ∈ ℝ^{N}, 2° a(x) → 1 as |x| → ∞, 3° there exist δ > 0 and C > 0 such that a(x) - 1 ≥ -Ce^{-(2+δ)|x|} for all x ∈ ℝ^{N}, 4° a(x) ≢ 1, we show that (*) has at least four positive solutions for sufficiently small ||f||_{H-1(ℝN)} but f ≢ 0.

Original language | English |
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Pages (from-to) | 63-95 |

Number of pages | 33 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 11 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2000 Aug |

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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