Existence of Positive Solutions for a Singular Hessian Equation with a Negative Augmented Term

• Xinguang Zhang ^[3] ; Peng Chen ^[1] ; Yonghong Wu ^[2] ; Benchawan Wiwatanapataphee ^[2]
  1. [1] Yantai University

     Yantai University

     China

     
  2. [2] Curtin University

     Curtin University

     Australia

     
  3. [3] Yantai University & Curtin University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we focus on the existence of positive solutions for a singular Hessian equation with a negative augmented term. By finding more appropriate upper and lower solutions, we not only overcome the difficulty due to the negative augmented term but also remove a critical condition required in the existing work and establish new results for the existence of positive solutions of the equations under study. Our results improve and complement many existing works.