Existence Results for p 1 ( x,·) and p 2 ( x,·) Fractional Choquard–Kirchhoff Type Equations with Variable s ( x,·)-Order

Weichun Bu, Tianqing An, Guoju Ye and Chengwen Jiao
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Weichun Bu: College of Science, Hohai University, Nanjing 211100, China
Tianqing An: College of Science, Hohai University, Nanjing 211100, China
Guoju Ye: College of Science, Hohai University, Nanjing 211100, China
Chengwen Jiao: College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China

Mathematics, 2021, vol. 9, issue 16, 1-20

Abstract: In this article, we study a class of Choquard–Kirchhoff type equations driven by the variable s ( x , · ) -order fractional p 1 ( x , · ) and p 2 ( x , · ) -Laplacian. Assuming some reasonable conditions and with the help of variational methods, we reach a positive energy solution and a negative energy solution in an appropriate space of functions. The main difficulties and innovations are the Choquard nonlinearities and Kirchhoff functions with the presence of double Laplace operators involving two variable parameters.

Keywords: Choquard–Kirchhoff type equations; fractional p 1 ( x ,·) and p 2 ( x ,·)-Laplacian; variational methods; positive energy solutions; negative energy solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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