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Existence and multiplicity of solutions for nonlocal systems with Kirchhoff type

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Abstract

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.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Zhi-tao Zhang

  2. School of Mathematics, Northwest University, Xi’an, 710127, China

    Yi-min Sun

Authors
  1. Zhi-tao Zhang
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  2. Yi-min Sun
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Correspondence to Yi-min Sun.

Additional information

Supported by the National Natural Science Foundation of China (No. 11325107,11271353, 11331010).

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Zhang, Zt., Sun, Ym. Existence and multiplicity of solutions for nonlocal systems with Kirchhoff type. Acta Math. Appl. Sin. Engl. Ser. 32, 35–54 (2016). https://doi.org/10.1007/s10255-016-0545-1

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  • DOI: https://doi.org/10.1007/s10255-016-0545-1

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