Existence of entire radial solutions to Hessian type system

Ji-xian, Cui

doi:10.1186/s13661-022-01612-2

Bound Value Probl

2022

DOI: 10.1186/s13661-022-01612-2

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Existence of entire radial solutions to Hessian type system

Cui Ji-xian

Abstract: In this paper, the Dirichlet problem of Hessian type system is studied. After converting the existence of an entire solution to the existence of a fixed point of a continuous mapping, the existence of entire radial solutions is established by Schaefer fixed point theorem.

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2024

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Necessary and sufficient conditions of entire sub-solutions for a (k1, k2)-type Hessian systems with gradient terms

Gao,

2024

Journal of Mathematical Physics

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In this paper, we aim to discuss a class of (k1, k2)-type Hessian system with gradient terms. In the case of k1 = k2 = 1 and 2 ≤ k1, k2 ≤ n, we obtain a sufficient and necessary condition for the existence of the entire admissible sub-solution of the system according to the value range of different parameters, which is also called the generalized Keller–Osserman condition. Based on this, we also discuss the conditions of existence and non-existence of the entire sub-solution, respectively. Finally, we extend the nonlinear terms to the degenerate case and consider the condition of the existence of the positive sub-solution for the above system.

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Necessary and sufficient conditions of entire sub-solutions for a (k1, k2)-type Hessian systems with gradient terms

Gao,

2024

Journal of Mathematical Physics

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Existence of entire radial solutions to Hessian type system

Abstract: In this paper, the Dirichlet problem of Hessian type system is studied. After converting the existence of an entire solution to the existence of a fixed point of a continuous mapping, the existence of entire radial solutions is established by Schaefer fixed point theorem.

Cited by 1 publication

References 19 publications

Necessary and sufficient conditions of entire sub-solutions for a (k1, k2)-type Hessian systems with gradient terms

Necessary and sufficient conditions of entire sub-solutions for a (k1, k2)-type Hessian systems with gradient terms

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