3 papers
math.AP2025
A new proof on quasilinear Schrödinger equations with prescribed mass and combined nonlinearities
Jianhua Chen, Jijiang Sun, Chenggui Yuan +1
In this work, we study the quasilinear Schrödinger equation \begin{equation*} \aligned -Δu-Δ(u^2)u=|u|^{p-2}u+|u|^{q-2}u+λu,\,\, x\in\R^N, \endaligned \end{equation*} under the mas…
math.AP2024
Asymptotic behavior of solutions for a critical heat equation with nonlocal reaction
Jian Zhang, Jacques Giacomoni, Vicentiu Radulescu +1
In this paper, we consider the following nonlocal parabolic equation \begin{equation*} u_{t}-Δu=\left( \int_Ω\frac{|u(y,t)|^{2^{\ast}_μ}}{|x-y|^μ}dy\right) |u|^{2^{\ast}_μ-2}u,\ \t…
math.AP2022
Normalized solutions to Kirchhoff type equations with a critical growth nonlinearity
Jian Zhang, Jianjun Zhang, Xuexiu Zhong
In this paper, we are concerned with normalized solutions of the Kirchhoff type equation \begin{equation*} -M\left(\int_{\R^N}|\nabla u|^2\mathrm{d} x\right)Δu = λu +f(u) \ \ \math…