Existence, regularity and positivity of ground states for nonlocal nonlinear Schrodinger equations
Date
2019-11-26
Authors
Zhang, Yong-Chao
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study ground states of a nonlinear Schrödinger equation driven by the infinitesimal generator of a rotationally invariant Levy process. The equation includes many special cases such as classical Schrodinger equations, fractional Schrödinger equations and relativistic Schrödinger equations, etc. It is proved that the equation possesses ground states in a suitable space of functions, then the regularity of solutions to the equation is examined, in particular, any solution is Hölder continuous, and, if the process involves diffusion terms, any solution is twice differentiable further. Finally, we show that any ground state is either positive or negative.
Description
Keywords
Nonlocal Schrödinger equation, Ground state, Infinitesimal generator, Rotationally invariant Levy process
Citation
Zhang, Y. C. (2019). Existence, regularity and positivity of ground states for nonlocal nonlinear Schrodinger equations. <i>Electronic Journal of Differential Equations, 2019</i>(128), pp. 1-11.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.