摘要
【目的】研究一类非局部问题在无界域上的可解性,探索其正解的存在性和多重性条件。【方法】利用Ekeland’s变分原理和山路引理等变分方法,分析该问题对应泛函的几何结构。【结果】获得了两个正解的存在性,其中一个是负能量解和一个是正能量解。【结论】结果表明,该类非局部问题具有变分结构,可以通过变分法技巧加以研究。此外,相关结果对相关领域的数学模型提供了理论支撑。
[Purposes]Consider the solvability of a class of nonlocal problems on unbounded domain and discuss the existence and multiplicity conditions of its positive solutions.[Methods]The geometric structure of the associated functional was analyzed by using the variational method of Ekeland＇s variational principle and Mountain pass lemma,and so on.[Findings]The existence of two positive solutions is obtained,which are a negative energy solution and a positive energy solution.[Conclusion]It is shown that these nonlocal problems have a variational structure.Therefore,they may be studied by some variational methods.In addition,the relevant results could provide a theoretical support for some mathematical models in related field.
出处
《重庆师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2018年第1期84-87,共4页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金(No.11661021)
贵州省教育厅创新群体重大研究项目(黔科合KY字[2016]029)
贵州民族大学科研基金(No.16yjsxm042)
