Results 31 to 40 of about 289,226 (165)

Normalized solutions for Sobolev critical fractional Schrödinger equation

open access: yesAdvances in Nonlinear Analysis
In the present study, we investigate the existence of the normalized solutions to Sobolev critical fractional Schrödinger equation: (−Δ)su+λu=f(u)+∣u∣2s*−2u,inRN,(Pm)∫RN∣u∣2dx=m2,\hspace{14em}\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+\lambda u=f ...
Li Quanqing   +3 more
doaj   +1 more source

Normalized solutions for Kirchhoff equations with Choquard nonlinearity: mass Super-Critical Case

open access: yesCommunications in Analysis and Mechanics
In the present paper, we investigated the existence of normalized solutions for the following Kirchhoff equation with Choquard nonlinearity$ \begin{equation*} -\Big(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}dx\Big)\Delta u-\lambda u = \mu|u|^{q-2}u+(I_ ...
Zhi-Jie Wang, Hong-Rui Sun
doaj   +1 more source

Non-singular solutions to the normalized Ricci flow equation [PDF]

open access: green, 2022
Fuquan Fang   +2 more
openalex   +1 more source

Multiple normalized solutions for Choquard equation involving the biharmonic operator and competing potentials in

open access: yesBulletin of Mathematical Sciences
This paper is concerned with the existence of multiple normalized solutions for a class of Choquard equation involving the biharmonic operator and competing potentials in [Formula: see text]: Δ2u+V(𝜀x)u=λu+G(𝜀x)(Iμ∗F(u))f(u)in ℝN,∫ℝN|u|2dx=c2, where ...
Shuaishuai Liang   +3 more
doaj   +1 more source

Normalized solutions for the Kirchhoff equation with combined nonlinearities in ℝ4

open access: yesAdvances in Nonlinear Analysis
In this article, we study the following Kirchhoff equation with combined nonlinearities: −a+b∫R4∣∇u∣2dxΔu+λu=μ∣u∣q−2u+∣u∣2u,inR4,∫R4∣u∣2dx=c2,\left\{\begin{array}{l}-\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{4}}{| \nabla u| }^{2}{\rm ...
Qiu Xin   +3 more
doaj   +1 more source

Multiplicity and concentration of normalized solutions for a Kirchhoff type problem with $ L^2 $-subcritical nonlinearities

open access: yesCommunications in Analysis and Mechanics
In this paper, we studied the existence of multiple normalized solutions to the following Kirchhoff type equation:$ \begin{equation*} \begin{cases} -\left(a\varepsilon^2+b\varepsilon\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+V(x)u = \mu u+f(u) &
Yangyu Ni, Jijiang Sun, Jianhua Chen
doaj   +1 more source

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