期刊
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
卷 72, 期 1, 页码 -出版社
SPRINGER INT PUBL AG
DOI: 10.1007/s00033-021-01472-3
关键词
Dirac equation; Generalized dual fountain theorem; Concave and convex nonlinearities; Non-periodic potential
资金
- National Science Foundation of China [NSFC11871242]
We prove the existence of infinitely many large and small energy solutions for non-periodic Dirac equations with nonlinearities involving a combination of concave and convex terms. A new critical point theorem is established for small energy solutions, which generalizes the dual Fountain Theorem of Bartsch and Willen. Non-periodic conditions on the whole space R-3 are given to overcome the lack of compactness.
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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