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In this paper, we study the following fractional Kirchhoff equation (a+b∫R3|(−Δ)s2u|2dx)(−Δ)su=λu+μ|u|q−2u+|u|p−2uinR3,with a prescribed mass ∫R3|u|2dx=c2,where s∈(34,1), a, b, c>0, 2<q<p<2s∗=63−2s, μ>0 and λ∈R as Lagrange multiplier. By decomposing Pohozaev set constructing fiber map, existence properties of normalized ground states are established.

In this paper, we are concerned with a fractional Kirchhoff equation general coercive potential. First, consider some existence and nonexistence of L2-constraint minimizers for related constrained minimization problems. Most importantly, by constructing appropriate trial functions delicate energy estimates studying decay properties solution sequences, then establish the concentration behaviors

We consider $L^{2}$ -constraint minimizers of the mass critical fractional Schrödinger energy functional with a ring-shaped potential $V(x)=(|x|-M)^{2}$ , where $M&gt;0$ and $x\in \mathbb {R}^{2}$ . By analysing some new estimates on least functional, we obtain concentration behaviour each minimizer when $a\nearrow a^{\ast }=\|Q\|_{2}^{2s}$ $Q$ is unique positive radial solution $(-\Delta )^{s}u+su-|u|^{2s}u=0$ in $\mathbb

&lt;abstract&gt;&lt;p&gt;This paper was concerned with the following Kirchhoff type equation involving fractional Laplace operator $ (-\Delta)^{s} $&lt;/p&gt; &lt;p&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE1"&gt; \begin{document}$ \begin{cases} \left(1+\alpha\int_{\mathbb{R}^{3}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right)(-\Delta)^{s} u+\mu K(x)u = g(x)|u|^{p-2}u, &amp;amp;{\rm in}\ \mathbb{R}^{3}, \\ u\in H^{s}(\mathbb{R}^{3}), \ \end{cases} $\end{document}...

In this paper, we study the following nonlinear Schrödinger-Bopp-Podolsky system: -, where p,q [?] (4,6), μ > 0, l(x), a(x) and b(x) are nonnegative continuous functions.Under some certain assumptions, prove above system have ground state multiple solutions by using variational.

In this article, we study a class of critical fractional Schrodinger-Poisson system with two perturbation terms. By using variational methods and Lusternik-Schnirelman category theory, the existence ground state nontrivial solutions are established.&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2021/07/abstr.html

In this paper, we study the following fractional Schrödinger–Poisson system where is Riesz potential, . By using a monotonicity trick and global compactness lemma, obtain existence of ground state solution for above system.

In this paper, we study the following nonlinear fractional Schrödinger-Poisson system <p class="disp_formula">$\begin{equation*}\left\{\begin{array}{ll}(-\Delta)^{s}u+\lambda V(x)u+\mu\phi u=|u|^{p-2}u, &amp; \hbox{in}\; \mathbb{R}^3 , \\(-\Delta)^{s}\phi=u^{2}, \mathbb{R}^3, \end{array}\right.\end{equation*}$ where <inline-formula><tex-math id="M1">\begin{document}$s\in(\frac{3}{4}, 1)$\end{document}</tex-math></inline-formula>, id="M2">\begin{document}$...

In this paper, we study the following fractional Schrödinger-Poisson system, and 2 * s = 6 3-2s is critical Sobolev exponent.By using a monotonicity argument global compactness lemma, obtain existence of ground state solution for system.

In this paper, we study the existence and asymptotic properties of solutions to following fractional Kirchhoff equation \begin{equation*} \left(a+b\int_{\mathbb{R}^{3}}|(-Δ)^{\frac{s}{2}}u|^{2}dx\right)(-Δ)^{s}u=λu+μ|u|^{q-2}u+|u|^{p-2}u \quad \hbox{in $\mathbb{R}^3$,} \end{equation*} with a prescribed mass \int_{\mathbb{R}^{3}}|u|^{2}dx=c^{2}, where $s\in(0, 1)$, $a, b, c&gt;0$, $20$ $λ\in\mathbb{R}$ as Lagrange multiplier. Under different assumptions on $q0$ $μ&gt;0$, prove some results...