Positive solutions for a Kirchhoff type problem with fast increasing weight and critical nonlinearity
In this paper, we study the following Kirchhoff type problem a + b Z R3 K(x)|∇u| 2 dx div(K(x)∇u) = λK(x)|x| |u| q−2u + K(x)|u| 4u, x ∈ R 3 where K(x) = exp(|x| α/4) with α ≥ 2, β = (α − 2)(6 − q)/4 and the parameters a, b, λ > 0. When 6 − 4 α < q < 6, we obtain a positive ground state solu...
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Kirchhoff típusú egyenlet, Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.27 |
| Online Access: | http://acta.bibl.u-szeged.hu/58090 |
| LEADER | 01255nas a2200217 i 4500 | ||
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| 005 | 20210916104230.0 | ||
| 008 | 190531s2019 hu o 0|| zxx d | ||
| 022 | |a 1417-3875 | ||
| 024 | 7 | |a 10.14232/ejqtde.2019.1.27 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a zxx | ||
| 100 | 1 | |a Qian Xiaotao | |
| 245 | 1 | 0 | |a Positive solutions for a Kirchhoff type problem with fast increasing weight and critical nonlinearity |h [elektronikus dokumentum] / |c Qian Xiaotao |
| 260 | |c 2019 | ||
| 300 | |a 1-17 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a In this paper, we study the following Kirchhoff type problem a + b Z R3 K(x)|∇u| 2 dx div(K(x)∇u) = λK(x)|x| |u| q−2u + K(x)|u| 4u, x ∈ R 3 where K(x) = exp(|x| α/4) with α ≥ 2, β = (α − 2)(6 − q)/4 and the parameters a, b, λ > 0. When 6 − 4 α < q < 6, we obtain a positive ground state solution for any λ > 0. When 2 < q < 4, we obtain a positive solution for λ > 0 small enough. In the proof we use variational methods. | |
| 695 | |a Kirchhoff típusú egyenlet, Differenciálegyenlet | ||
| 700 | 0 | 1 | |a Chao Wen |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/58090/1/ejqtde_2019_027.pdf |z Dokumentum-elérés |