Existence and concentration behavior of ground state solutions for magnetic nonlinear Choquard equations

We letΩ(r)be the axially symmetric bounded domains which satisfy some suitable conditions, then the ground-state solutions of the semilinear elliptic equation inΩ(r)are nonaxially symmetric and concentrative on one side. Furthermore, we prove the necessary and sufficient condition for the symmetry of ground-state solutions.

Download Full-text

Concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system involving critical exponent

Communications in Contemporary Mathematics ◽

10.1142/s021919971850027x ◽

2019 ◽

Vol 21 (06) ◽

pp. 1850027 ◽

Cited By ~ 3

Author(s):

Zhipeng Yang ◽

Yuanyang Yu ◽

Fukun Zhao

Keyword(s):

Small Parameter ◽

Critical Exponent ◽

Ground State ◽

Local Minimum ◽

Fractional Laplacian ◽

Ground State Solution ◽

Critical Nonlinearity ◽

Poisson System ◽

Ground State Solutions ◽

Concentration Behavior

We are concerned with the existence and concentration behavior of ground state solutions of the fractional Schrödinger–Poisson system with critical nonlinearity [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text], [Formula: see text], [Formula: see text] denotes the fractional Laplacian of order [Formula: see text] and satisfies [Formula: see text]. The potential [Formula: see text] is continuous and positive, and has a local minimum. We obtain a positive ground state solution for [Formula: see text] small, and we show that these ground state solutions concentrate around a local minimum of [Formula: see text] as [Formula: see text].

Download Full-text

The concentration behavior of ground state solutions for nonlinear Dirac equation

Nonlinear Analysis ◽

10.1016/j.na.2019.111738 ◽

2020 ◽

Vol 195 ◽

pp. 111738 ◽

Cited By ~ 1

Author(s):

Yanheng Ding ◽

Yuanyang Yu

Keyword(s):

Dirac Equation ◽

Ground State ◽

Ground State Solutions ◽

Nonlinear Dirac Equation ◽

Concentration Behavior

Download Full-text

Ground States for Mass Critical Two Coupled Semi-Relativistic Hartree Equations with Attractive Interactions

10.22541/au.163954547.70856317/v1 ◽

2021 ◽

Author(s):

Thi-Anh-Thu DOAN

Keyword(s):

Ground State ◽

Energy Estimates ◽

Boson Stars ◽

Precise Description ◽

Ground State Solutions ◽

Blowing Up ◽

Existence And Nonexistence ◽

Normalized Solutions ◽

Bose Einstein ◽

Concentration Behavior

We prove the existence and nonexistence of $L^{2}(\mathbb R^3)$-normalized solutions of two coupled semi-relativistic Hartree equations, which arisen from the studies of boson stars and multi-component Bose–Einstein condensates. Under certain condition on the strength of intra-specie and inter-specie interactions, by proving some delicate energy estimates, we give a precise description on the concentration behavior of ground state solutions of the system. Furthermore, an optimal blowing up rate for the ground state solutions of the system is also proved.

Download Full-text