10 papers · 1 filter
Normalized solutions to critical and supercritical Schrödinger equations in a ball
Jun Wang, Zhaoyang Yin
In this paper, we study radial normalized solutions to nonlinear Schrödinger equations in the unit ball \[ -Δu+λu=|u|^{p-1}u, \qquad \int_{B_1}|u|^2\,dx=ρ, \] where is unknown…
Existence and dependency results for coupled Schrödinger equations with critical exponent on waveguide manifold
Jun Wang, Zhaoyang Yin
We study the coupled Schrödinger equations with critical exponent on . With the help of scaling argument and semivirial-vanishing technology, we obt…
Transverse dependence and asymptotic dimensional reduction of ground states for the logarithmic Schrödinger equation on a waveguide manifold
Hichem Hajaiej, Jun Wang, Zhaoyang Yin
In this paper, we develop a novel approach to studying the -dependence of ground states for the logarithmic Schrödinger equation on . Unlike in \…
Orbital stability of normalized ground states for critical Choquard equation with potential
Jun Wang, Zhaoyang Yin
In this paper, we study the existence of ground state standing waves and orbital stability, of prescribed mass, for the nonlinear critical Choquard equation \begin{equation*} \left…
Almost sure well-posedness and orbital stability for Schrödinger equation with potential
Jun Wang, Zhaoyang Yin
In this paper, we study the almost sure well-posedness theory and orbital stability for the nonlinear Schrödinger equation with potential \begin{equation*} \left\{\begin{array}{l}…
Normalized solutions and stability for biharmonic Schrödinger equation with potential on waveguide manifold
Jun Wang, Zhaoyang Yin
In this paper, we study the following biharmonic Schrödinger equation with potential and mixed nonlinearities \begin{equation*} \left\{\begin{array}{ll}Δ^2 u +V(x,y)u+λu =μ|u|^{p-2…
Global well-posedness, scattering and blow-up for the energy-critical, Schrödinger equation with indefinite potential in the radial case
Jun Wang, Zhaoyang Yin
In this paper, we study the well-posedness theory and the scattering asymptotics for the energy-critical, Schrödinger equation with indefinite potential \begin{equation*} \left\{\b…
Global well-posedness, scattering and blow-up for the energy-critical, Schrödinger equation with general nonlinearity in the radial case
Jun Wang, Zhaoyang Yin
In this paper, we study the well-posedness theory and the scattering asymptotics for the energy-critical, Schrödinger equation with general nonlinearity \begin{equation*} \left\{\b…
Multi-bump solutions for the nonlinear magnetic Schrödinger equation with logarithmic nonlinearity
Jun Wang, Zhaoyang Yin
In this paper, we study the following nonlinear magnetic Schrödinger equation with logarithmic nonlinearity \begin{equation*} -(\nabla+iA(x))^2u+λV(x)u =|u|^{q-2}u+u\log |u|^2,\ u\…
Normalized solutions for Schödinger equations with potential and general nonlinearities involving critical case on large convex domains
Jun Wang, Zhaoyang Yin
In this paper, we study the following Schrödinger equations with potentials and general nonlinearities \begin{equation*} \left\{\begin{aligned} & -Δu+V(x)u+λu=|u|^{q-2}u+βf(u), \\…