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- Title
Multiple positive solutions for a nonlinear elliptic equation involving Hardy-Sobolev-Maz'ya term.
- Authors
Peng, Shuang; Yang, Jing
- Abstract
In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz'ya term: where Ω is a bounded domain in ℝ ( N ≥ 2), 0 ∈ Ω, x = ( y, z) ∈ ℝ × ℝ and $p_t = \frac{{N + 2 - 2t}} {{N - 2}}(0 \leqslant t \leqslant 2)$ For f( x) ∈ C( $\bar \Omega $){0}, we show that there exists a constant μ* > 0 such that the problem possesses at least two positive solutions if μ ∈ (0, μ*) and at least one positive solution if μ = μ*. Furthermore, there are no positive solutions if μ ∈ (μ*,+∞).
- Subjects
ELLIPTIC equations; EXISTENCE theorems; MATHEMATICAL constants; MOUNTAIN pass theorem; MATHEMATICAL inequalities
- Publication
Acta Mathematica Sinica, 2015, Vol 31, Issue 6, p893
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-015-4230-8