数学物理学报 ›› 2024, Vol. 44 ›› Issue (2): 384-395.

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一类超线性 $k$-Hessian 方程耦合系统的径向解

高承华(),丁欢欢*(),何兴玥()   

  1. 西北师范大学数学与统计学院 兰州 730070
  • 收稿日期:2023-01-25 修回日期:2023-09-05 出版日期:2024-04-26 发布日期:2024-04-07
  • 通讯作者: * 丁欢欢,Email:hding_nwnu@163.com
  • 作者简介:高承华,Email:gaokugou@163.com;何兴玥,Email:hett199527@163.com
  • 基金资助:
    国家自然科学基金(11961060);甘肃省优秀研究生创新之星科研项目(2023CXZX-323);西北师范大学研究生科研基金(2022KYZZ-S112)

Radial Solutions of Coupled Systems for a Class of Superlinear $ k$-Hessian Equations

Gao Chenghua(),Ding Huanhuan*(),He Xingyue()   

  1. Department of Mathematics, Northwest Normal University, Lanzhou 730070
  • Received:2023-01-25 Revised:2023-09-05 Online:2024-04-26 Published:2024-04-07
  • Supported by:
    NSFC(11961060);Excellent Graduate Student Innovation Star Scientific Research Project of Gansu Province(2023CXZX-323);Graduate Research Support of Northwest Normal University(2022KYZZ-S112)

摘要:

研究一类带参数的奇异超线性 $k$-Hessian 系统 Dirichlet 问题解的存在性. 基于 Banach 空间中的 Krasnosel'skii 型不动点定理, 建立了非平凡径向解的存在性、多解性及不存在性结果. 同时, 讨论了解依赖于参数的渐近行为.

关键词: 径向解, Dirichlet 问题, 耦合 $k$-Hessian 方程, Krasnosel'skii 型不动点定理

Abstract:

The existence of solutions to Dirichlet problems for a class of singular superlinear $k$-Hessian systems with parameters is studied. Based on the Krasonsel'skii type fixed point theorem in a Banach space, the existence, multiplicity and nonexistence results of nontrivial radial solutions are obtained. At the same time, the asymptotic behavior dependent on parameter is discussed.

Key words: Radial solution, Dirichlet problem, Coupled $k$-Hessian equations, Krasonsel'skii type fixed point theorem

中图分类号: 

  • O175.8