Multiple positive solutions for a nonlinear elliptic equation involving Hardy-Sobolev-Maz'ya term
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| 024 | 7 | 0 | |a 10.1007/s10114-015-4230-8 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4230-8 | ||
| 245 | 0 | 0 | |a Multiple positive solutions for a nonlinear elliptic equation involving Hardy-Sobolev-Maz'ya term |h [Elektronische Daten] |c [Shuang Peng, Jing Yang] |
| 520 | 3 | |a In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz'ya term: $ - \Delta u - \lambda \frac{u} {{|y|^2 }} = \frac{{|u|^{p_t - 1} u}} {{|y|^t }} + \mu f(x),x \in \Omega ,$ where Ω is a bounded domain in ℝ N (N ≥ 2), 0 ∈ Ω, x = (y, z) ∈ ℝ k × ℝ N-k and $p_t = \frac{{N + 2 - 2t}} {{N - 2}}(0 \leqslant t \leqslant 2)$ For f(x) ∈ C 1( $\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*,+∞). | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Hardy-Sobolev-Maz'ya inequality |2 nationallicence | |
| 690 | 7 | |a Mountain Pass Lemma |2 nationallicence | |
| 690 | 7 | |a positive solutions |2 nationallicence | |
| 690 | 7 | |a subsolution and supersolution |2 nationallicence | |
| 700 | 1 | |a Peng |D Shuang |u School of Mathematics and Statistics, Central China Normal University, 430079, Wuhan, P. R. China |4 aut | |
| 700 | 1 | |a Yang |D Jing |u School of Mathematics and Statistics, Central China Normal University, 430079, Wuhan, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/6(2015-06-01), 893-912 |x 1439-8516 |q 31:6<893 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4230-8 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4230-8 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Peng |D Shuang |u School of Mathematics and Statistics, Central China Normal University, 430079, Wuhan, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Yang |D Jing |u School of Mathematics and Statistics, Central China Normal University, 430079, Wuhan, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/6(2015-06-01), 893-912 |x 1439-8516 |q 31:6<893 |1 2015 |2 31 |o 10114 | ||