Positive solutions for a Kirchhoff type problem with fast increasing weight and critical nonlinearity

Qian, Xiaotao and Chao, Wen: Positive solutions for a Kirchhoff type problem with fast increasing weight and critical nonlinearity. Electronic journal of qualitative theory of differential equations 27. pp. 1-17. (2019)

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Abstract

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.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 27
Page Range: pp. 1-17
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.27
Uncontrolled Keywords: Kirchhoff típusú egyenlet, Differenciálegyenlet
Additional Information: Bibliogr.: p. 15-17. ; összefoglalás angol nyelven
Date Deposited: 2019. May. 31. 05:09
Last Modified: 2019. May. 31. 05:10
URI: http://acta.bibl.u-szeged.hu/id/eprint/58090

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