Results 11 to 20 of about 3,355,287 (250)

Normalized solutions for the p-Laplacian equation with a trapping potential

Advances in Nonlinear Analysis, 2023
In this article, we are concerned with normalized solutions for the pp -Laplacian equation with a trapping potential and Lr{L}^{r}-supercritical growth, where r=pr=p or 2.2.
Wang Chao, Sun Juntao
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The existence and multiplicity of the normalized solutions for fractional Schrödinger equations involving Sobolev critical exponent in the L2-subcritical and L2-supercritical cases

Advances in Nonlinear Analysis, 2022
This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: (P)(−Δ)su+λu=μ∣u∣p−2u+∣u∣2s∗−2u,x∈RN,u>0,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}{\left(-\Delta )}^{s}u+\lambda
Li Quanqing, Zou Wenming
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Normalized solutions for a critical fractional Choquard equation with a nonlocal perturbation

Advances in Nonlinear Analysis, 2023
In this article, we study the fractional critical Choquard equation with a nonlocal perturbation: (−Δ)su=λu+α(Iμ*∣u∣q)∣u∣q−2u+(Iμ*∣u∣2μ,s*)∣u∣2μ,s*−2u,inRN,{\left(-{\Delta })}^{s}u=\lambda u+\alpha \left({I}_{{\mu }^{* }}\hspace{-0.25em}{| u| }^{q}){| u|
Lan Jiali, He Xiaoming, Meng Yuxi
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Normalized solutions for Sobolev critical fractional Schrödinger equation

Advances 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, Nie Jianjun, Wang Wenbo, Zhou Jianwen   +3 more
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Normalized solutions for a fractional coupled critical Hartree system [PDF]

Electronic Journal of Qualitative Theory of Differential Equations
We consider the existence of normalized solutions for a fractional coupled Hartree system, with the upper critical exponent in the sense of the Hardy-Littelwood-Sobolev inequality.
Shengbing Deng, Wenshan Luo
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Normalized solutions for the double-phase problem with nonlocal reaction

Advances in Nonlinear Analysis
In this article, we consider the double-phase problem with nonlocal reaction. For the autonomous case, we introduce the methods of the Pohozaev manifold, Hardy-Littlewood Sobolev subcritical approximation, adding the mass term to prove the existence and ...
Cai Li, Zhang Fubao
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Normalized solutions of NLS equations with mixed nonlocal nonlinearities

Advances in Nonlinear Analysis
We study the existence and nonexistence of normalized solutions for the nonlinear Schrödinger equation with mixed nonlocal nonlinearities: −Δu=λu+μ(Iα∗∣u∣p)∣u∣p−2u+(Iα∗∣u∣q)∣u∣q−2uinRN,∫RN∣u∣2dx=c,\left\{\begin{array}{ll}-\Delta u=\lambda u+\mu \left({I ...
Zhang Zhenyu, Sun Juntao
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Normalized solutions for the discrete Schrödinger equations

Boundary Value Problems, 2023
In the present paper, we consider the existence of solutions with a prescribed l 2 $l^{2}$ -norm for the following discrete Schrödinger equations, { − Δ 2 u k − 1 − f ( u k ) = λ u k k ∈ Z , ∑ k ∈ Z | u k | 2 = α 2 , $$ \textstyle\begin{cases} -\Delta ...
Qilin Xie, Huafeng Xiao
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Normalized concentrating solutions to nonlinear elliptic problems [PDF]

, 2021
We prove the existence of solutions (λ,v)∈R×H1(Ω) of the elliptic problem {−Δv+(V(x)+λ)v=vp in Ω,v>0,∫Ωv2dx=ρ. Any v solving such problem (for some λ) is called a normalized solution, where the normalization is settled in L2(Ω).
Pellacci B., Vaira G., Pistoia A., Verzini G.   +3 more
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Normalized solutions to the Schrödinger systems with double critical growth and weakly attractive potentials

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper, we look for solutions to the following critical Schrödinger system $$\begin{cases} -\Delta u+(V_1+\lambda_1)u=|u|^{2^*-2}u+|u|^{p_1-2}u+\beta r_1|u|^{r_1-2}u|v|^{r_2}&{\rm in}\ \mathbb{R}^N,\\ -\Delta v+(V_2+\lambda_2)v=|v|^{2^*-2}v+|v ...
Lei Long, Xiaojing Feng
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