The Existence and Blow-Up of the Radial Solutions of a (k1, k2)-Hessian System Involving a Nonlinear Operator and Gradient
The Existence and Blow-Up of the Radial Solutions of a (k1, k2)-Hessian System Involving a Nonlinear Operator and Gradient
复制标题
DOI：
10.1007/s10473-022-0409-0
复制
发表时间：
2022-04
影响因子：
1
通讯作者：
Guotao Wang;Zedong Yang;Jiafa Xu;Lihong Zhang
中科院分区：
文献类型：
--
作者：
Guotao Wang;Zedong Yang;Jiafa Xu;Lihong Zhang
本文研究了（k 1，k 2）-Hessian系统{G（K 1 1 k 1）K 1 1 k 1= B 1（|2）k = 1（1）k = 1（1）k = 1（1）k = 1（1）k = B（|X|）g2（z1，z2），x∈ <$N，其中G是一个非线性算子，Ki = Ski（λ（D2 zi））+<$i（|X|)|拉吉齐|ki，i= 1，2.在g1和g2上的适当条件下，利用单调迭代法和Arzela-Ascoli定理得到了我们的主要结果.此外，我们的主要结果也推广了以前的单方程和系统的存在性结果。
In this paper, we are concerned with the existence of the positive bounded and blow-up radial solutions of the (k 1, k 2)-Hessian system {G (K 1 1 k 1) K 1 1 k 1= b 1 (| x∣) g 1 (z 1, z 2), x∈ ℝ N, G (K 2 1 k 2) K 2 1 k 2= b 2 (| x|) g 2 (z 1, z 2), x∈ ℝ N, where G is a nonlinear operator, K i= S ki (λ (D 2 zi))+ ψ i (| x|)|∇ zi| ki, i= 1, 2. Under the appropriate conditions on g 1 and g 2, our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem. Furthermore, our main results also extend the previous existence results for both the single equation and systems.