Nonexistence of entire positive solutions for conformal Hessian quotient inequalities

  • Received: 01 April 2021 Revised: 01 July 2021 Published: 22 September 2021
  • Primary: 35J60, 35B08; Secondary: 35B09

  • In this paper, we consider the nonexistence problem for conformal Hessian quotient inequalities in $ \mathbb{R}^n $. We prove the nonexistence results of entire positive $ k $-admissible solution to a conformal Hessian quotient inequality, and entire $ (k, k') $-admissible solution pair to a system of Hessian quotient inequalities, respectively. We use the contradiction method combining with the integration by parts, suitable choices of test functions, Taylor's expansion and Maclaurin's inequality for Hessian quotient operators.

    Citation: Feida Jiang, Xi Chen, Juhua Shi. Nonexistence of entire positive solutions for conformal Hessian quotient inequalities[J]. Electronic Research Archive, 2021, 29(6): 4075-4086. doi: 10.3934/era.2021072

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  • In this paper, we consider the nonexistence problem for conformal Hessian quotient inequalities in $ \mathbb{R}^n $. We prove the nonexistence results of entire positive $ k $-admissible solution to a conformal Hessian quotient inequality, and entire $ (k, k') $-admissible solution pair to a system of Hessian quotient inequalities, respectively. We use the contradiction method combining with the integration by parts, suitable choices of test functions, Taylor's expansion and Maclaurin's inequality for Hessian quotient operators.



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