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Minkowski空间中含一类推广的平均曲率算子系统的正径向解存在唯一性
Existence and Uniqueness of Positive Radial Solutions for a Class of Generalized Mean Curvature Operator Systems in Minkowski Space

DOI: 10.12677/pm.2026.162050, PP. 208-217

Keywords: 推广的平均曲率算子，Dirichlet问题，径向正解，锥上不动点指数理论，Leggett-Williams不动点定理
Generalized Mean Curvature Operator, Dirichlet Problem, Positive Radial Solutions, Fixed Point Index Theory in Cones, Leggett-Williams Fixed Point Theorem

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Abstract:

本文运用锥上不动点指数理论探讨含一类推广的平均曲率算子的拟线性微分系统Dirichlet问题 ( H ){ M k ( u )+ f 1 ( v )=0？,？x∈ ？ 1 M k ( v )+ f 2 ( u )=0？,？x∈ ？ 1 u| ？ ？ 1 = v| ？ ？ 1 =0 径向正解的存在性和唯一性，其中 M k ( u )=div( ？u ( 1？ | ？u | 2 ) k 2 )( k≥1 ) ，

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