Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1357-1371.

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Existence and Asymptotic Behavior of Solutions of a Class of k-Hessian Equation

Lihong Zhang1(),Zedong Yang1(),Guotao Wang1,2,*(),Dumitru Baleanu3,4()   

  1. 1 School of Mathematics and Computer Science, Shanxi Normal University, Shanxi Linfen 041004
  • Received:2020-11-07 Online:2021-10-26 Published:2021-10-08
  • Contact: Guotao Wang;;;
  • Supported by:
    the NSFC(11501342);the NSFC(12001344);the Graduate Education Innovation Program Fund of Shanxi(2020SY337)


In this paper, we consider the following boundary blow-up $k$-Hessian problem where $\Omega \subset \mathbb{R} ^{N}$ is a smooth, bounded, strictly convex domain. We are concerned with the existence of the radially symmetric positive solutions of the $k$-Hessian equation and obtain new boundary asymptotic behavior of strictly convex blow-up positive solutions of the $k$-Hessian equation. Our approach mainly relies on the monotone iterative method, the upper and lower solution method and Karamata regular variation theory.

Key words: Asymptotic behavior, k-Hessian equation, Positive radial solution, Keller-Osserman condition, Karamata regular variation theory

CLC Number: 

  • O175