Existence and multiplicity of solutions for nonlocal systems with Kirchhoff type

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• 作者：Zhi-tao Zhang ; Yi-min Sun
• 关键词：Critical point ; Nehari manifold ; cohomological index
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：32
• 期：1
• 页码：35-54
• 全文大小：334 KB
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• 作者单位：Zhi-tao Zhang (1)
  Yi-min Sun (2)
  
  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  2. School of Mathematics, Northwest University, Xi’an, 710127, China
  
• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

Firstly, we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type. Then a multiplicity result is established by cohomological index of Fadell and Rabinowitz. We also consider the critical case and prove existence of positive least energy solution when the parameter β is sufficiently large.