7 papers
Mountain-Pass Solutions for Second-Order Ergodic Mean-Field Game Systems
Fanze Kong, Yonghui Tong, Xiaoyu Zeng
We study the existence of mountain-pass solutions to a potential-free mean-field game system in the whole space under the mass-supercritical regime, assuming an aggre…
Gagliardo-Nirenberg-Sobolev inequalities and ground states of Fermions in relativistic Hartree-Fock model
Yuan-da Wu, Xiaoyu Zeng, Yimin Zhang
This paper presents a rigorous mathematical analysis of the relativistic Hartree-Fock model for finite Fermi systems. We first establish an optimal Gagliardo-Nirenberg-Sobolev (GNS…
Existence and Blow-up Profiles of Ground States in Second Order Multi-population Mean-field Games Systems
Fanze Kong, Juncheng Wei, Xiaoyu Zeng
In this paper, we utilize the variational structure to study the existence and asymptotic profiles of ground states in multi-population ergodic Mean-field Games systems subject to…
Local Minimizers in Second Order Mean-field Games Systems with Choquard Coupling
Fanze Kong, Yonghui Tong, Xiaoyu Zeng
Mean-field Games systems (MFGs) serve as paradigms to describe the games among a huge number of players. In this paper, we consider the ergodic Mean-field Games systems in the boun…
Critical Mass Phenomena and Blow-up behavior of Ground States in stationary second order Mean-Field Games systems with decreasing cost
Marco Cirant, Fanze Kong, Juncheng Wei +1
This paper is devoted to the study of Mean-field Games (MFG) systems in the mass critical exponent case. We firstly establish the optimal Gagliardo-Nirenberg type inequality associ…
Co-existence of Type II blow-ups with multiple blow-up rates for five-dimensional heat equation with critical nonlinear boundary conditions
Juncheng Wei, Zikai Ye, Xiaoyu Zeng +1
We consider the following five-dimensional heat equation with critical boundary condition \begin{equation*} \partial_t u=Δu \mbox{ \ in \ } \mathbb{R}_+^5\times (0,T) , \quad -\par…
Infinitely many solutions for a class of fractional Schrodinger equations coupled with neutral scalar field
Liejun Shen, Marco Squassina, Xiaoyu Zeng
We study the fractional Schrödinger equations coupled with a neutral scalar field $$ (-Δ)^s u+V(x)u=K(x)ϕu +g(x)|u|^{q-2}u, \quad x\in \mathbb{R}^3,\qquad (I-Δ)^t ϕ=K(x)u^2, \quad…