非周期Dirac方程的稳态解

Stationary solutions of non-periodic Dirac equations

本文研究Dirac方程-iΣαkku+aβu+M(x)u=g(x,|u|)u的解,其中M(x)是位势函数,g(x,|u|)u在无穷远处关于u是超线性的.本文用变分法来研究这一问题.借助于与此方程的"极限方程"相关的某个辅助系统,构造了变分泛函ΦM的环绕水平,使得建立在ΦM环绕结构上的极小极大值CM满足0<CM<C,这里C是"极限方程"的最小能量.从而可以证明(C)c条件对所有c<C成立,因此得到了方程的最小能量解.

This paper is concerned with solutions to the Dirac equation：-iΣαkku＋aβu＋M（x）u=g（x,｜u｜）u.Here M（x） is a general potential and g（x,｜u｜）u is super linear in u at infinity.We use variational methods to study this problem.By virtue of some auxiliary system related to the ＂limit equation＂ of the Dirac equation,we constructed linking levels of the variational functional ΦM such that the minimax value CM based on the linking structure of ΦM satisfies 0 CM C,where C is the least energy of the ＂limit equation＂.Thus we can show the（C）c-condition holds true for all c C and consequently,we obtain one least energy solution of the Dirac equation.