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 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 1-17 |
| ISSN: | 1417-3875 |