摘要
通过构造函数的方法获得一类带线性指数非局部Kirchhoff型问题的无穷多解,直观表明它们有的是正解,有的是负解,有的是变号解;另外,本文还获得一般条件下存在无穷多个收敛到零的古典解,以此表明非平凡解的不稳定性.与采用变分方法和山路引理得到的结论比较,其对应的能量泛函收敛到同一个非零常数,近共振解对应的能量泛函收敛到零.在现有文献的基础上扩宽了研究范围并获得了更好的结论。
The existence of infinitely many solutions for a nonlocal Kirchhoff type problem with linear exponent is obtained by the constructors of functions,and for those solutions,we found some of them are positive solutions,some are negative solutions and some are sign-changing solutions.Besides,there exist infinitely many classical solutions which converge to zero in general condition,their energy functional are converge to a nozero constant,and the functional are converge to zero for solutions near resonances,by compared with the results which come from the variational methods and mountain pass lemma.The results we mentioned above show the instability of the nontrivial solutions.The area of our research is widely and we obtain a better conclusion based on the existing literatures.
作者
王艳红
王跃
索洪敏
WANG YanHong;WANG Yue;SUO Hongmin(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China;School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)
出处
《南昌大学学报（理科版）》
CAS
北大核心
2020年第4期323-327,共5页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金资助项目(11661021,11861021)
贵州省科技厅科研基金(黔科合基础[2016]1074,黔科合基础[2019]1163)
贵州民族大学引进人才科研资助项目(校引才科研[2018]019)。
关键词
线性指数
非局部问题
无穷多解
近共振
infinitely many classical solutions
linear exponent
nonlocal problem
constructor of function
near resonance
