Classification of nonnegative solutions to static Schrodinger-Hartree and Schrodinger-Maxwell equations with combined nonlinearities
Classification of nonnegative solutions to static Schrodinger-Hartree and Schrodinger-Maxwell equations with combined nonlinearities
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具有组合非线性的静态薛定谔-哈特里和薛定谔-麦克斯韦方程非负解的分类
DOI：
10.1007/s00526-019-1595-z
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发表时间：
2019
影响因子：
2.1
通讯作者：
Liu Zhao
中科院分区：
文献类型：
--
作者：
Dai Wei;Liu Zhao
本文研究了具有组合非线性项的静态Schr dinger-Hartree和Schr dinger-Maxwell方程.我们得到了临界情形下正解的显式形式和次临界情形下非平凡非负解的不存在性（见定理\ref{Thm 0}和\ref{Thm 1}）.在我们的证明中使用的参数是一个变种（非局部非线性）的直接移动球方法的分数拉普拉斯\cite{CLZ}。主要成分是最大值原理的变体（对于非局部非线性），即，窄域原理（Thm 2和Thm 3定理）。
In this paper, we are concerned with static Schr\"{o}dinger-Hartree and Schr\"{o}dinger-Maxwell equations with combined nonlinearities. We derive the explicit forms for positive solutionin the critical case and non-existence of nontrivial nonnegative solutions in the subcritical cases (see Theorem \ref{Thm0} and \ref{Thm1}). The arguments used in our proof is a variant (for nonlocal nonlinearity) of the direct moving spheres method for fractional Laplacians in \cite{CLZ}. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., \emph{Narrow region principle} (Theorem \ref{Thm2} and \ref{Thm3}).