Infinitely many solutions of Dirac equations with concave and convex nonlinearities

被引：7
|
作者：
Ding, Yanheng [1 ]
Dong, Xiaojing [1 ,2 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Beijing 100049, Peoples R China
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2021年 / 72卷 / 01期
基金：
美国国家科学基金会;
关键词：
Dirac equation; Generalized dual fountain theorem; Concave and convex nonlinearities; Non-periodic potential; STATIONARY STATES; EXISTENCE;
D O I：
10.1007/s00033-021-01472-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider non-periodic Dirac equations with nonlinearities which involve a combination of concave and convex terms. Using variational methods, we prove the existence of infinitely many large and small energy solutions. For small energy solutions, we establish a new critical point theorem which generalize the dual Fountain Theorem of Bartsch and Willen, by using the index theory and the P-topology. Some non-periodic conditions on the whole space R-3 are given in order to overcome the lack of compactness.
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页数：17
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