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Existence and nonexistence of solutions for a class of Kirchhoff type equation involving fractional p-Laplacian
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 2.9 ) Pub Date : 2020-06-30 , DOI: 10.1007/s13398-020-00893-5 Senli Liu , Haibo Chen , Jie Yang , Yu Su
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 2.9 ) Pub Date : 2020-06-30 , DOI: 10.1007/s13398-020-00893-5 Senli Liu , Haibo Chen , Jie Yang , Yu Su
In this paper, we consider the following Kirchhoff type equation involving the fractional p-Laplacian: $$\begin{aligned} \begin{aligned} M \left( \iint _{\mathbb {R}^{2N}} \frac{|u(x)-u(y)|^{p}}{|x-y|^{N+sp}} \mathrm {d}x\mathrm {d}y \right) (-\Delta )^{s}_{p} u +\lambda V(x)|u|^{p-2}u =K(x)f(u), \;x\in \mathbb {R}^{N}, \end{aligned} \end{aligned}$$ where $$\lambda $$ is a real parameter, $$\left( -\Delta \right) ^{s}_{p}$$ is the fractional p-Laplacian operator, with $$0
中文翻译：
一类包含分数p-Laplacian的Kirchhoff型方程解的存在与不存在
在本文中，我们考虑以下涉及分数 p-Laplacian 的 Kirchhoff 型方程： $$\begin{aligned} \begin{aligned} M \left( \iint _{\mathbb {R}^{2N}} \frac {|u(x)-u(y)|^{p}}{|xy|^{N+sp}} \mathrm {d}x\mathrm {d}y \right) (-\Delta )^{ s}_{p} u +\lambda V(x)|u|^{p-2}u =K(x)f(u), \;x\in \mathbb {R}^{N}, \ end{aligned} \end{aligned}$$ 其中 $$\lambda $$ 是实参数， $$\left( -\Delta \right) ^{s}_{p}$$ 是分数 p-Laplacian运营商，$0
更新日期：2020-06-30
中文翻译：
一类包含分数p-Laplacian的Kirchhoff型方程解的存在与不存在
在本文中，我们考虑以下涉及分数 p-Laplacian 的 Kirchhoff 型方程： $$\begin{aligned} \begin{aligned} M \left( \iint _{\mathbb {R}^{2N}} \frac {|u(x)-u(y)|^{p}}{|xy|^{N+sp}} \mathrm {d}x\mathrm {d}y \right) (-\Delta )^{ s}_{p} u +\lambda V(x)|u|^{p-2}u =K(x)f(u), \;x\in \mathbb {R}^{N}, \ end{aligned} \end{aligned}$$ 其中 $$\lambda $$ 是实参数， $$\left( -\Delta \right) ^{s}_{p}$$ 是分数 p-Laplacian运营商，$0
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