在非齐次边界条件下一类非齐次Schr(o)dinger-Poisson系统的多个解

摘要

In this paper, a class of Schrodinger-Poisson systems with nonhomogeneous nonlinear pertuxbable term under inhomoge-neous boundary condition is studied. Schrbdinger-Poisson systems are very important mathematical physical equations. These systems are very importantly meaningful in physics, which describe the motion of charged particals in an electromagnetic field, especially describe a charged partical interacting with unkown potential in its owner electromagnetic field. Many kinds of these systems with homogeneous boundary condition have been discussed, but systems with nonhomogeneous nonlinear perturbable term under inhomogeneous boundary condition are not still discussed. Thus the study in this paper is necessary in view of mathematical point. Consequently, the existence result of multiple solutions for this system is obtained by Ekeland variation principle and Mountain-Pass Lemma.%研究了具有非齐次非线性扰动项和非齐次边界条件的一类Schr(o)dinger-Poisson系统.Schr(o)dinger -Poisson系统是非常重要的数学物理方程组,这类系统在物理上有很重要的意义,描述了带电粒子在电磁场运动,特别是在未给定势的电磁场里的相互作用.这类系统在其次边界条件下的各类情况均有人讨论,但在非齐次边界条件下具有非齐次非线性扰动项的此类系统没有讨论.于是从数学的角度可以看出此研究是必要的.主要用Ekeland变分原理和山路引理得到了此类Schr(o)dinger-Poisson系统多个解的存在性结果.