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Semi-linear Liouville theorems in the generalized Greiner vector fields

Author

Listed:
  • Yazhou Han

    (China Jiliang University)

  • Qiong Zhao

    (China Jiliang University)

  • Yongyang Jin

    (Zhejiang University of Technology)

Abstract

This paper is devoted to study a class of semi-linear elliptic equation with principal part constructed by generalized Greiner vector fields. Using the idea of vector field method, we introduce a new functional for generalized Greiner vector fields. Through many identity deformations and accurate estimates, a class of Liouville type theorem is given. It improves the Liouville type theorem obtained by Niu etc., which can be seen in Canad. Math. Bull., 47(3), 417–430 (2004).

Suggested Citation

  • Yazhou Han & Qiong Zhao & Yongyang Jin, 2013. "Semi-linear Liouville theorems in the generalized Greiner vector fields," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(3), pages 311-342, June.
    • Handle: RePEc:spr:indpam:v:44:y:2013:i:3:d:10.1007_s13226-013-0016-9
    DOI: 10.1007/s13226-013-0016-9
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    Cited by:

    1. Wei Shi, 2022. "Liouville-Type Theorem for Nonlinear Elliptic Equations Involving Generalized Greiner Operator," Mathematics, MDPI, vol. 11(1), pages 1-10, December.

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