The Keller–Osserman Problem for the k-Hessian Operator

Covei, Dragoş-Pătru

doi:10.1007/s00025-020-1174-9

Cited by 7 publications

(3 citation statements)

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“…Jin, Li and Xu [20] investigated the viscosity subsolutions for the equation k (D 2 u) = u p in the whole space R n or in the half space R n + . In this paper, we extend the results in [20] to the equation (8). Let g(x, t) be defined on ∂R n + × [0, ∞) such that g(x, t) > 0 for any x ∈ ∂R n + and t > 0.…”

Section: Introduction the Augmented Hessian Equationmentioning

confidence: 82%

“…Covei [8] studied the Keller-Osserman condition on the boundary blow up solution of Hessian equations. The Keller-Osserman condition on the existence of entire solutions is similar to that on the existence of boundary blow up solutions, we can also refer to [11].…”

Section: Introduction the Augmented Hessian Equationmentioning

confidence: 99%

“…Proofs of Theorem 1.2 and Theorem 1.3. First, we give the definition of viscosity solutions to (8). One can also refer to [9,20].…”

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confidence: 99%

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Existence and nonexistence of subsolutions for augmented Hessian equations

Dai¹

2020

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper, we consider the augmented Hessian equationsWe first give the necessary and sufficient condition of the existence of classical subsolutions to the equations in R n for σ(x) = α, which is an extended Keller-Osserman condition. Then we obtain the nonexistence of positive viscosity subsolutions of the equations in R n or R n + for f (u) = u p with p > 1.2010 Mathematics Subject Classification. 35J60, 35D40.

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Section: Introduction the Augmented Hessian Equationmentioning

confidence: 82%

Section: Introduction the Augmented Hessian Equationmentioning

confidence: 99%