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Ground state solutions for the nonlinear fractional Schrodinger-Poisson system
TL;DR: In this article, the existence of ground state solutions for the nonlinear fractional Dinger-Poisson system was studied and a nontrivial ground state solution was established through using a monotonicity trick and global compactness Lemma.
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Abstract: In this paper, we study the existence of ground state solutions for the nonlinear fractional Schr\"{o}dinger-Poisson system \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^su+V(x)u+\phi u=|u|^{p-1}u, & \hbox{in $\mathbb{R}^3$,} (-\Delta)^s\phi=u^2,& \hbox{in $\mathbb{R}^3$,} \end{array} \right. \end{equation*} where $2<p<2_s^{\ast}-1 = \frac{3+2s}{3-2s}$, $s\in(\frac{3}{4},1)$. Under certain assumptions on $V$, a nontrivial ground state solution $(u,\phi)$ is established through using a monotonicity trick and global compactness Lemma. As its supplementary results, we prove some nonexistence results in the case of $1<p\leq 2$ and $p=2_s^{\ast}-1$.
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Citations
Existence and Concentration of Solutions for a Class of Elliptic Kirchhoff–SchrödingerEquations with Subcritical and Critical Growth
TL;DR: In this paper, the existence and concentration of ground state solutions for a class of fractional Kirchhoff-Schrodinger equations was studied. But the authors focused on the existence of ground-state solutions with minimal energy for a large value of γ ≥ 0.
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Positive Solutions for Schrödinger-Poisson Systems with Sign-Changing Potential and Critical Growth
TL;DR: In this article, the existence and multiplicity of positive solutions for Schrodinger-Poisson systems with sign-changing potential and critical growth was studied. But the existence of positive solution was not investigated.
Ground State Solutions of Fractional Choquard Problems with Critical Growth
17 Jul 2023
TL;DR: In this paper , the existence of ground state solutions for a class of fractional Choquard equations with critical Sobolev exponent was investigated and a monotonicity technique and global compactness lemma was obtained.
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