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

Author

Listed:
  • Weichun Bu

    (College of Science, Hohai University, Nanjing 211100, China
    College of Science, Zhongyuan University of Technology, Zhengzhou 450007, 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)

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.

Suggested Citation

  • Weichun Bu & Tianqing An & Guoju Ye & Chengwen Jiao, 2021. "Existence Results for p 1 ( x ,·) and p 2 ( x ,·) Fractional Choquard–Kirchhoff Type Equations with Variable s ( x ,·)-Order," Mathematics, MDPI, vol. 9(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1973-:d:616689
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