关于带双临界项的薛定谔-泊松方程  

SchrÖdinger Poisson equations with double-critical terms

作　　者：刘增[1] LIU Zeng(School of Mathematical Sciences,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2021年第2期17-26,共10页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11901418,11771319)。

摘　　要：研究一类带双临界项的薛定谔-泊松方程-Δu+u+μ(I_(2)*|u|^(5))|u|^(3)u-λ|u|^(p-2)u-|u|^(4)u=0 in R^(3),其中p∈(2,6),λ≥0,μ>0,I_(2)(x):=(4π|x|)^(-1)是Riesz位势,*表示卷积。利用变分方法,证明方程正径向对称解的存在性及非存在性,并研究解关于参数λ的渐近性态。We studied the SchrÖdinger Poisson equations with double critical terms-Δu+u+μ(I_(2)*|u|^(5))|u|^(3)u-λ|u|^(p-2)u-|u|^(4)u=0 in R^(3),where p∈(2,6)and λ≥0,μ>0,I_(2)(x):=(4π|x|)^(-1) is the Riesz potential and *denotes the standard convolution.The existence and nonexistence of positive radially symmetric solutions were obtained by using variational methods.We also explored the asymptotic behaviors of solutions with respect to the parameter λ.

关 键 词：薛定谔-泊松方程 临界非局部项 波霍扎耶夫恒等式 变分法 

分 类 号：O175.2[理学—数学]