Zhi-You Chen

On the Classification of Standing Wave Solutions for the Schrödinger Equation

In this article, we consider the following semilinear elliptic equation where n ≥ 3, p > 1 and λ > 0. We provide the existence and uniqueness of the singular radial solution of the above equation for specific ranges of n and p. In addition, we also clarify the entire structure of radial solutions for various types according to their behaviors at the origin and infinity.

Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations

In this article, we are concerned with the semilinear elliptic equation where n > 2, p > 1, and K(lxl) > 0 in R n . The correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived. In addition, we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on K and p. Furthermore, based on the Pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions, we obtain the whole structure of radial solutions depending on various situations.

The solution structure of the O(3) sigma model in a Maxwell-Chern-Simons theory

In this paper, a system of semilinear elliptic equations arising from a relativistic self-dual Maxwell-Chern-Simons O(3) sigma model is considered. We reveal the uniqueness aspect of the topological solutions for the model. The uniqueness result is associated with a clear solution structure of the equations of the radially symmetric case. We locate each solution set denoted by a planar diagram.

Topological multivortex solutions for the Chern–Simons system with two Higgs particles

ABSTRACT In this paper, we prove the uniqueness of topological multivortex solutions to the self-dual abelian Chern–Simons model if either the Chern–Simons coupling parameter is sufficiently small or sufficiently large. In addition, we also establish the sharp region of the flux for nontopological solutions with a single vortex point.

Erratum to “On the Classification of Standing Wave Solutions for the Schrödinger Equation”

In [1], Lemma 3.2 guaranteed the monotonicity of regular solutions of (1.4) on some fixed interval near the origin in terms of initial values, so as to prove the existence of singular solutions of (1.1). To make the arguments more clear for readers, the estimate of g t on page 295, line 23 in the original proof of Lemma 3.2 needs to be modified. Here, we provide a revised statement and proof of this lemma, and add an extra remark in the following. Refer to [1] for all notations and labeled equations appearing below.