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Infinitely Many Solutions for Fractional p-Kirchhoff Equations

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In this paper we consider the existence of infinitely many weak solutions for fractional Schrödinger–Kirchhoff problems. Precisely speaking, we investigate $$\begin{aligned} \left\{ \begin{array}{cl} M\left( \int _{\mathbb {R}^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\mathrm{d}x\mathrm{d}y\right) (-\triangle )_p^su+V(x)|u|^{p-2}u=f(x,u), &{}\quad… Click to show full abstract

In this paper we consider the existence of infinitely many weak solutions for fractional Schrödinger–Kirchhoff problems. Precisely speaking, we investigate $$\begin{aligned} \left\{ \begin{array}{cl} M\left( \int _{\mathbb {R}^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\mathrm{d}x\mathrm{d}y\right) (-\triangle )_p^su+V(x)|u|^{p-2}u=f(x,u), &{}\quad \mathrm{in}~\Omega ,\\ u=0, &{}\quad \mathrm{in}~\mathbb {R}^n\setminus \Omega , \end{array}\right. \end{aligned}$$M∫R2n|u(x)-u(y)|p|x-y|n+spdxdy(-▵)psu+V(x)|u|p-2u=f(x,u),inΩ,u=0,inRn\Ω,where $$\Omega $$Ω is a bounded subset with Lipshcitz boundary $$\partial \Omega $$∂Ω, $$0

Keywords: kirchhoff; solutions fractional; many solutions; infinitely many; fractional kirchhoff; mathrm

Journal Title: Mediterranean Journal of Mathematics
Year Published: 2018

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