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Critical fractional Schrödinger-Poisson systems with lower perturbations: the existence and concentration behavior of ground state solutions

open access: yesAdvances in Nonlinear Analysis
In this article, we study the following fractional Schrödinger-Poisson system: ε2s(−Δ)su+V(x)u+ϕu=f(u)+∣u∣2s*−2u,inR3,ε2t(−Δ)tϕ=u2,inR3,\left\{\begin{array}{ll}{\varepsilon }^{2s}{\left(-\Delta )}^{s}u+V\left(x)u+\phi u=f\left(u)+{| u| }^{{2}_{s}^{* }-2 ...
Feng Shenghao   +2 more
doaj   +1 more source

Normalized solutions of Schrödinger equations involving Moser-Trudinger critical growth

open access: yesAdvances in Nonlinear Analysis
In this article, we are concerned with the nonlinear Schrödinger equation −Δu+λu=μ∣u∣p−2u+f(u),inR2,-\Delta u+\lambda u=\mu {| u| }^{p-2}u+f\left(u),\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{2}, having prescribed ...
Li Gui-Dong, Zhang Jianjun
doaj   +1 more source
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Energy Estimate Related to a Hardy-Trudinger-Moser Inequality

Journal of Partial Differential Equations, 2019
Let B1 be a unit disc of R2, and H be a completion of C∞ 0 (B1) under the norm ∥u∥H = ∫ B1 ( |∇u|2− u 2 (1−|x|2)2 ) dx. Using blow-up analysis, Wang-Ye [1] proved existence of extremals for a Hardy-TrudingerMoser inequality.
Yunyan Yang sci
semanticscholar   +1 more source

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