一类双相问题多重解的存在性  

Multiple Solutions for a Class of Double Phase Problem

作　　者：钱正雅 王智勇[1] QIAN Zhengya;WANG Zhiyong(School of Mathematics and Satistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《应用数学》2023年第2期400-408,共9页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11571176,11701289);Jiangsu Province Science Foundation for Youths(BK20170936)。

摘　　要：本文研究一类双相问题多重解的存在性.基于变分方法,证明了该问题至少存在两个非平凡解.当非线性项关于u是奇函数,利用对称山路引理,我们同时得到了该问题存在无穷多对解.In this paper,we deal with the existence of multiple nontrivial solutions for a class of double phase problem.Based on variational methods,we prove the existence of at least two nontrivial solutions for this problem.Moreover,if the nonlinearity is odd in u,we also obtain infinitely many pairs of solutions via symmetry mountain pass theorem.

关 键 词：双相问题 山路定理 EKELAND变分原理 对称山路定理 

分 类 号：O175.12[理学—数学]