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math.AP2024
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…
math.AP2024
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…
math.AP2024
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…