Entire large solutions to the k-Hessian equations with weights: Existence, uniqueness and asymptotic behavior

Wan, Haitao; Shi, Yongxiu; Qiao, Xiaoyan

doi:10.1016/j.jmaa.2021.125301

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Introduction and The Main Results1

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2024

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Cited by 9 publications

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“…More results on the existence, uniqueness and asymptotic behavior of boundary blow-up solutions to (1.1) in the bounded domain see [5,8,10,16,20,22,25]. Other works of entire solutions to the Monge-Ampère or Hessian equation, see [4,7,11,26].…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Song

Quan

et al. 2021

Asymptotic Analysis

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The aim of this paper is to consider the following fractional parabolic problem u t + ( − Δ ) p α u + ( − Δ ) q β u = f ( x , u ) ( x , t ) ∈ Ω × ( 0 , ∞ ) , u = 0 ( x , t ) ∈ ( R N ∖ Ω ) × ( 0 , ∞ ) , u ( x , 0 ) = u 0 ( x ) x ∈ Ω , where Ω ⊂ R N is a bounded domain with Lipschitz boundary, ( − Δ ) p α is the fractional p-Laplacian with 0 < α < 1 < p < ∞, ( − Δ ) q β is the fractional q-Laplacian with 0 < β < α < 1 < q < p < ∞, r > 1 and λ > 0. The global existence of nonnegative solutions is obtained by combining the Galerkin approximations with the potential well theory. Then, by virtue of a differential inequality technique, we give a decay estimate of solutions.

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Section: Introduction and The Main Resultsmentioning

confidence: 99%

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Song

Quan

et al. 2021

Asymptotic Analysis

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show abstract

Entire positive p-k-convex radial solutions to p-k-Hessian equations and systems

Kan

Zhang

2023

Lett Math Phys

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Existence and asymptotic behavior of nontrivial p-k-convex radial solutions for p-k-Hessian equations

Feng,

2024

Lett Math Phys

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Entire large solutions to the k-Hessian equations with weights: Existence, uniqueness and asymptotic behavior

Cited by 9 publications

References 45 publications

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Entire positive p-k-convex radial solutions to p-k-Hessian equations and systems

Existence and asymptotic behavior of nontrivial p-k-convex radial solutions for p-k-Hessian equations

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