Results 1 to 10 of about 8,874,290 (299)

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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A comprehensive review on the existence of normalized solutions for four classes of nonlinear elliptic equations [PDF]

Opuscula Mathematica
This paper provides a comprehensive review of recent results concerning the existence of normalized solutions for four classes of nonlinear elliptic equations: Schrödinger equations, Schrödinger-Poisson equations, Kirchhoff equations, and Choquard ...
Sitong Chen, Xianhua Tang
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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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Normalized solutions to a Choquard equation involving mixed local and nonlocal operators [PDF]

Nonlinear Differential Equations and Applications
In the present paper, we study the existence of normalized solutions for a Choquard type equation involving mixed diffusion type operators. We also provide regularity results of these solutions.
Jacques Giacomoni, Giacomoni J, Sreenadh K   +2 more
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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 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 the Choquard equations with critical nonlinearities

Advances in Nonlinear Analysis
This study is concerned with the existence of normalized solutions for the Choquard equations with critical nonlinearities −Δu+λu=f(u)+(Iα∗∣u∣2α*)∣u∣2α*−2u,inRN,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}-\Delta u+\lambda u=f\left(u)+\left({I}_{\alpha }\ast ...
Gao Qian, He Xiaoming
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Normalized solutions for fractional Schrodinger-Choquard systems with Sobolev critical coupled nonlinearity

Electronic Journal of Differential Equations
We study the existence of normalized solutions for a system of fractional Schrodinger-Choquard with Sobolev critical coupling term. We obtain the existence of the positive normalized ground state solution, and in a special case we obtain a mountain ...
Zilin Chen, Yang Yang
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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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