Results 1 to 10 of about 628 (105)

Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth

Advances in Nonlinear Analysis, 2020
In this paper, we study the singularly perturbed fractional Choquard ...
Yang Zhipeng, Zhao Fukun
doaj   +2 more sources

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
doaj   +2 more sources

Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian

Advances in Mathematical Physics
In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N≥3, F represents the primitive function of f,  f∈CR;R is a function that fulfils the general ...
Sarah Abdullah Qadha, Muneera Abdullah Qadha, Haibo Chen, Yuying Zao   +3 more
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Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation

Advances in Nonlinear Analysis, 2020
In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard ...
Binhua Feng, Chen Ruipeng, Liu Jiayin
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Ground State Solutions of Fractional Choquard Problems with Critical Growth

Fractal and Fractional, 2023
In this article, we investigate a class of fractional Choquard equation with critical Sobolev exponent. By exploiting a monotonicity technique and global compactness lemma, the existence of ground state solutions for this equation is obtained.
Jie Yang, Hongxia Shi
doaj   +1 more source

Linear Barycentric Rational Method for Solving Schrodinger Equation

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
A linear barycentric rational collocation method (LBRCM) for solving Schrodinger equation (SDE) is proposed. According to the barycentric interpolation method (BIM) of rational polynomial and Chebyshev polynomial, the matrix form of the collocation method (CM) that is easy to program is obtained.
Peichen Zhao, Yongling Cheng, Ram Jiwari
wiley   +1 more source

Existence of Solutions for Choquard Type Elliptic Problems with Doubly Critical Nonlinearities

Advanced Nonlinear Studies, 2021
In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in ℝN{\mathbb{R}^{N}} involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential.
Shen Yansheng
doaj   +1 more source

On nonlinear fractional Choquard equation with indefinite potential and general nonlinearity

Boundary Value Problems, 2023
In this paper, we consider a class of fractional Choquard equations with indefinite potential ( − Δ ) α u + V ( x ) u = [ ∫ R N M ( ϵ y ) G ( u ) | x − y | μ d y ] M ( ϵ x ) g ( u ) , x ∈ R N , $$ (-\Delta )^{\alpha}u+V(x)u= \biggl[ \int _{{\mathbb{R ...
Fangfang Liao, Fulai Chen, Shifeng Geng, Dong Liu   +3 more
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Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity

Mathematics, 2019
In this paper, we study a class of nonlinear Choquard equation driven by the fractional Laplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state solution for the fractional Choquard equation by using a non ...
Huxiao Luo, Shengjun Li, Chunji Li
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The Existence of Normalized Solutions for a Nonlocal Problem in ℝ3

Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020
In this paper, we study the following fractional Schrödinger equation in ℝ3(−Δ)σu − λu = |u|p−2u, in ℝ3 with σ ∈ (0, 1), λ ∈ ℝ and p ∈ (2 + σ, 2 + (4/3)σ). By using the constrained variational method, we show the existence of solutions with prescribed L2 norm for this problem.
Jing Yang, Dimitrios Tsimpis
wiley   +1 more source