一类藕合k-Hessian 系统非线性径向k-凸解的渐近行为
The Asymptotic Behavior of Nontrivial Radial k-Convex Solutions for a Class of Coupled k-Hessian System
DOI: 10.12677/AAM.2022.117522, PDF, HTML, 下载: 234  浏览: 326 
作者: 岳存燕*：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 藕合k-Hessian系统；非线性径向k-凸解；渐近行为；不动点定理；Coupled k-Hessian System； Nontrivial Radial k-Convex Solution； Asymptotic Behavior； Fixed-Point Theorem
摘要: 基于锥上的不动点定理，本文主要研究一类藕合k-Hessian 系统非线性径向k-凸解的渐近行为。
Abstract: Based on the fixed-point theorem in cone, we study the asymptotic behavior of non- trivial radial k-convex solutions for a class of coupled k-Hessian system.
文章引用：岳存燕. 一类藕合k-Hessian 系统非线性径向k-凸解的渐近行为[J]. 应用数学进展, 2022, 11(7): 4979-4989. https://doi.org/10.12677/AAM.2022.117522

参考文献

[1] Trudinger, N. and Wang, X. (2008) The Monge-Amp`ere Equations and Its Geometric Appli- cations. Handbook of Geometric Analysis, 1, 467-524.
[2] Shivaji, R., Sim, I. and Son, B. (2017) A Uniqueness Result for a Semipositone p-Laplacian Problem on the Exterior of a Ball. Journal of Mathematical Analysis and Applications, 445, 459-475.
https://doi.org/10.1016/j.jmaa.2016.07.029
[3] Zhang, Z. (2015) Boundary Behavior of Large Solutions to the Monge-Amp`ere Equations with Weight. Journal of Differential Equations, 259, 2080-2100.
https://doi.org/10.1016/j.jde.2015.03.040
[4] Zhang, Z. (2018) Large Solutions to the Monge-Amp`ere Equations with Nonlinear Gradient Terms: Existence and Boundary Behavior. Journal of Differential Equations, 264, 263-296.
https://doi.org/10.1016/j.jde.2017.09.010
[5] Zhang, Z. and Qi, Z. (2015) On a Power-Type Coupled of Monge-Amp`ere Equations. Topolog- ical Methods in Nonlinear Analysis, 46, 717-729.
[6] Lazer, A. and McKenna, P. (1996) On Singular Boundary Value Problems for the Monge Amp`ere Operator. Journal of Mathematical Analysis and Applications, 197, 342-362.
https://doi.org/10.1006/jmaa.1996.0024
[7] Feng, M. (2021) Convex Solutions of Monge-Amp`ere Equations and Systems: Existence, U- niqueness and Asymptotic Behavior. Advances in Nonlinear Analysis, 10, 371-399.
https://doi.org/10.1515/anona-2020-0139
[8] Feng, M. and Zhang, X. (2021) A Coupled System of k-Hessian Equations. Mathematical Methods in the Applied Sciences, 44, 7377-7394.
https://doi.org/10.1002/mma.6053
[9] Gao, C., He, X. and Ran, M. (2021) On a Power-Type Coupled System of k-Hessian Equations. Quaestiones Mathematicae, 44, 1593-1612.
https://doi.org/10.2989/16073606.2020.1816586
[10] Zhang, X. and Feng, M. (2019) The Existence and Asymptotic Behavior of Boundary Blow-Up Solutions to the k-Hessian Equation. Journal of Differential Equations, 267, 4626-4672.
https://doi.org/10.1016/j.jde.2019.05.004
[11] Wan, H., Shi, Y. and Qiao, X. (2021) Entire Large Solutions to the k-Hessian Equations with Weights: Existence, Uniqueness and Asymptotic Behavior. Journal of Mathematical Analysis and Applications, 503, Article ID: 125301.
https://doi.org/10.1016/j.jmaa.2021.125301
[12] Sun, H. and Feng, M. (2018) Boundary Behavior of k-Convex Solutions for Singular k-Hessian Equations. Nonlinear Analysis, 176, 141-156.
https://doi.org/10.1016/j.na.2018.06.010
[13] Trudinger, N. (1995) On the Dirichlet Problem for Hessian Equations. Acta Mathematica, 175, 151-164.
https://doi.org/10.1007/BF02393303
[14] Ji, X. and Bao, J. (2010) Necessary and Sufficient Condition on Solvability for Hessian Inequal- ities. Proceedings of the AMS, 138, 175-188.
https://doi.org/10.1090/S0002-9939-09-10032-1
[15] Guo, D. and Lakshmikantham, V. (1988) Nonlinear Problems in Abstract Cones. Academic Press, Inc., Cambridge, MA.

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