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Existence and Uniqueness of Solutions for the p ( x )-Laplacian Equation with Convection Term

Author

Listed:
  • Bin-Sheng Wang

    (College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China)

  • Gang-Ling Hou

    (College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China)

  • Bin Ge

    (College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China)

Abstract

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.

Suggested Citation

  • Bin-Sheng Wang & Gang-Ling Hou & Bin Ge, 2020. "Existence and Uniqueness of Solutions for the p ( x )-Laplacian Equation with Convection Term," Mathematics, MDPI, vol. 8(10), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1768-:d:427339
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    References listed on IDEAS

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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    3. Weihong Xie & Haibo Chen, 2018. "Existence and multiplicity of solutions for p(x)‐Laplacian equations in RN," Mathematische Nachrichten, Wiley Blackwell, vol. 291(16), pages 2476-2488, November.
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