含奇异梯度项的p-k-Hessian系统爆破解的存在性和非存在性

吉林大学学报(理学版) ›› 2026, Vol. 64 ›› Issue (4): 743-0750.

含奇异梯度项的p-k-Hessian系统爆破解的存在性和非存在性

杨泽栋¹, 白占兵²

1. 忻州师范学院数学系, 山西忻州 034000; 2. 山东科技大学数学与系统科学学院, 山东青岛 266590

收稿日期:2025-12-12 出版日期:2026-07-26 发布日期:2026-07-26
通讯作者: 白占兵 E-mail:zhanbingbai@163.com

Existence and Nonexistence of Blow-Up Solutions for p-k-Hessian System with Singular Gradient Terms

Yang Zedong¹, Bai Zhanbing²

1. Department of Mathematics, Xinzhou Normal University, Xinzhou 034000, Shanxi Province, China; 2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong Province, China

Received:2025-12-12 Online:2026-07-26 Published:2026-07-26

摘要/Abstract

摘要： 利用单调迭代方法, 研究一类含有奇异梯度项的p-k-Hessian系统p-k-凸径向解的存在性和有界性, 并给出有界解的范围估计. 在关于非线性项的适当假设条件下, 得到爆破解的存在性和非存在性, 并给出几个实例验证所得结论.

关键词: p-k-Hessian系统, 奇异梯度项, 爆破解, 非存在性

Abstract: By using the monotonic iterative method, we studied the existence and boundedness of p-k-convex radial solutions for a class of
p-k-Hessian systems with singular gradient terms, and gave the range estimate of bounded solutions. Under appropriate assumptions about nonlinear terms, we obtained the existence and nonexistence of blow-up solutions, and gave several examples to verify the obtained conclusions.

Key words: p-k-Hessian system, singular gradient term, blow-up solution, nonexistence

中图分类号:

O175.8

杨泽栋, 白占兵. 含奇异梯度项的p-k-Hessian系统爆破解的存在性和非存在性[J]. 吉林大学学报(理学版), 2026, 64(4): 743-0750.

Yang Zedong, Bai Zhanbing. Existence and Nonexistence of Blow-Up Solutions for p-k-Hessian System with Singular Gradient Terms[J]. Journal of Jilin University Science Edition, 2026, 64(4): 743-0750.