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math.AP2020
Normalized solutions of mass supercritical Schrödinger equations with potential
Thomas Bartsch, Riccardo Molle, Matteo Rizzi +1
This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation \[ -Δu+V(x)u+λu = |u|^{p-2}u \qquad\text{in } \] in the mass…
math.AP2020★ 4 cited
Strongly localized semiclassical states for nonlinear Dirac equations
Thomas Bartsch, Tian Xu
We study semiclassical states of the nonlinear Dirac equation \[ -i\hbar\partial_tψ= ic\hbar\sum_{k=1}^3α_k\partial_kψ- mc^2βψ- M(x)ψ+ f(|ψ|)ψ,\quad t\in\mathbb{R},\ x\in\mathbb{R}…