Existence of solutions for Kirchhoff type systems involving Q-Laplacian operator in Heisenberg group
Existence of solutions for Kirchhoff type systems involving Q-Laplacian operator in Heisenberg group
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DOI：
10.1016/j.jmaa.2020.124727
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发表时间：
2021-03
影响因子：
1.3
通讯作者：
Shengbing Deng;Xingliang Tian
中科院分区：
文献类型：
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作者：
Shengbing Deng;Xingliang Tian
设Hn是Heisenberg群，Q= 2n + 2是Hn的齐次维数，我们研究了下列Q-Laplacian椭圆方程组{− K（<$Ω）}解的存在性|∇ H n u| Q d）Δ Q u= λ G u（，u，v）ρ（）in Ω;− K（Ω| n v|其中Ω是Heisenberg群Hn的一个开的、光滑的有界子集，K是Kirchhoff型函数，0≤ <$< Q，λ是正参数，非线性项Gu，Gv具有临界指数增长性，其行为类似于exp <$（β| S| Q（1）作为|S| →+∞，某些β> 0。
Let H n be the Heisenberg group, Q= 2 n+ 2 be the homogeneous dimension of H n, we study the existence of solutions for the following Q-Laplacian elliptic system {− K (∫ Ω|∇ H n u| Q d ξ) Δ Q u= λ G u (ξ, u, v) ρ (ξ)℘ in Ω;− K (∫ Ω|∇ H n v| Q d ξ) Δ Q v= λ G v (ξ, u, v) ρ (ξ)℘ in Ω; u= 0, v= 0, on∂ Ω, where Ω is an open, smooth and bounded subset of Heisenberg group H n, K is a Kirchhoff type function, 0≤℘< Q and λ is a positive parameter, and nonlinear terms G u, G v have critical exponential growth behave like exp(β| s| Q Q− 1) as| s|→+∞ with some β> 0.