On a power-type coupled system of <i>k</i>-Hessian equations

Gao, Chenghua; He, Xingyue; Ran, Maojun

doi:10.2989/16073606.2020.1816586

Cited by 14 publications

(4 citation statements)

References 28 publications

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“…[32,12,25,38]), fixed point theorems (cf. [33,9,20,14]), the monotone iteration technique (cf. [35,2,37]), the variational method (cf.…”

Section: Introductionmentioning

confidence: 99%

Radial solutions for a class of multiparameter singular k-Hessian systems

Ding,

Gao,

2023

Preprint

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This paper is devoted to studying the coupled system of multiparameter k-Hessian equations S_k(\mu(D^2u_1))=\lambda_1\rho_1(|x|)f_1(-u_1,-u_2) in B, S_k(\mu(D^2u_2))=\lambda_2\rho_2(|x|)f_2(-u_1,-u_2) in B, u_1=u_2=0 on \partial B, where B=\{x\in\mathbb{R}^n:|x|<1\}, \lambda_1,\lambda_2 are positive parameters, \rho_i\,(i=1,2) is singular near the boundary \partial B, f_i\,(i=1,2) satisfies a combined superlinear condition at \infty. Employing the fixed point theorem of Krasnosel'skii type in Banach space, the existence and multiplicity of nontrivial radial solutions are established. In particular, the dependence of the solutions on the parameters \lambda_1,\lambda_2 is also discussed. Finally, we study the nonexistence results of nontrivial radial solutions for the case \lambda_1,\lambda_2\gg1. Mathematics Subject Classification (2010). 34B15, 34B18.

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“…[32,12,25,38]), fixed point theorems (cf. [33,9,20,14]), the monotone iteration technique (cf. [35,2,37]), the variational method (cf.…”

Section: Introductionmentioning

confidence: 99%

Radial solutions for a class of multiparameter singular k-Hessian systems

Ding,

Gao,

2023

Preprint

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“…For other results concerning the existence, nonexistence, and multiplicity of k-admissible solutions for a k-Hessian equation, we refer the reader to [11][12][13][14][15][16][17][18][19][20][21] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence and multiplicity of radially symmetric k-admissible solutions for a k-Hessian equation

Miao

2022

Bound Value Probl

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In this paper, we show that the radially symmetric k-admissible solutions set of a k-Hessian equation Dirichlet problem with homogeneous boundary condition contains a reversed S-shaped connected component. By determining the shape of unbounded continua of the solutions, we obtain the existence and multiplicity of radially symmetric k-admissible solutions with respect to the bifurcation parameter λ. The proof is based on the bifurcation technique.

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“…We refer to the papers of Feng and Zhang [6] and Gao, He, and Ran [7] and the references therein for research on coupling k-Hessian system (1.4) when μ = ν = 0. By the way, on general k-Hessian equation (1.2) and general coupling k-Hessian system (1.4) when μ = ν = 0, Zhang and Zhou [20] obtained several results on the existence of entire positive k-convex radial solutions.…”

Section: Introductionmentioning

confidence: 99%