Existence and concentration of ground state solutions for doubly critical Schrödinger–Poisson-type systems

Feng, Xiaojing

doi:10.1007/s00033-020-01381-x

Cited by 7 publications

(1 citation statement)

References 48 publications

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“…$$ By using the mountain pass theorem and the concentration‐compactness principle, Liu obtained the existence of a positive solution for (). Feng 14 studied the existence of positive solutions to () with the critical nonlinearity

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, by the modified concentration‐compactness principle and Nehari manifold method. Li and He 15 studied the existence and multiplicity of positive solutions for () by using the Ljusternik‐Schnirelmann theory.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Ground states for critical fractional Schrödinger‐Poisson systems with vanishing potentials

Dou

2022

Math Methods in App Sciences

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This paper deals with a class of fractional Schrödinger‐Poisson system {array(−Δ)su+V(x)u−K(x)ϕ|u|2s∗−3u=a(x)f(u),arrayx∈ℝ3array(−Δ)sϕ=K(x)|u|2s∗−1,arrayx∈ℝ3$$ \left\{\begin{array}{cc}{\left(-\Delta \right)}^su+V(x)u-K(x)\phi {\left|u\right|}^{2_s^{\ast }-3}u=a(x)f(u),\kern0.30em & x\in {\mathbb{R}}^3\\ {}{\left(-\Delta \right)}^s\phi =K(x){\left|u\right|}^{2_s^{\ast }-1},\kern0.30em & x\in {\mathbb{R}}^3\end{array}\right. $$ with a critical nonlocal term and multiple competing potentials, which may decay and vanish at infinity, where s∈false(34,1false),0.1em2s∗=63−2s$$ s\in \left(\frac{3}{4},1\right),{2}_s^{\ast }=\frac{6}{3-2s} $$ is the fractional critical exponent. The problem is set on the whole space, and compactness issues have to be tackled. By employing the mountain pass theorem, concentration‐compactness principle, and approximation method, the existence of a positive ground state solution is obtained under appropriate assumptions imposed on V$$ V $$, K$$ K $$, a$$ a $$, and f$$ f $$.

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f\left(x,u\right)&#x0003D;{\left&#x0007C;u\right&#x0007C;}&#x0005E;4u&#x0002B;g(u)

Section: Introduction and Main Resultsmentioning

confidence: 99%

Ground states for critical fractional Schrödinger‐Poisson systems with vanishing potentials

Dou

2022

Math Methods in App Sciences

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Multiplicity of normalized solutions for the fractional Schrödinger-Poisson system with doubly critical growth

Meng,

2024

Acta Math Sci

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On a Fractional Schrödinger–Poisson System with Doubly Critical Growth and a Steep Potential Well

Lan

2023

J Geom Anal

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Existence and concentration of ground state solutions for doubly critical Schrödinger–Poisson-type systems

Cited by 7 publications

References 48 publications

Ground states for critical fractional Schrödinger‐Poisson systems with vanishing potentials

Ground states for critical fractional Schrödinger‐Poisson systems with vanishing potentials

Multiplicity of normalized solutions for the fractional Schrödinger-Poisson system with doubly critical growth

On a Fractional Schrödinger–Poisson System with Doubly Critical Growth and a Steep Potential Well

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