一类半线性双曲型微分不等式非齐次 Dirichlet 外问题解的存在性与非存在性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (5): 1167-1182.

一类半线性双曲型微分不等式非齐次 Dirichlet 外问题解的存在性与非存在性

肖苏平¹,赵元章^2,^*()

¹山西师范大学数学与计算机科学学院太原 030000
²中国海洋大学数学科学学院山东青岛 266100

收稿日期:2023-10-04 修回日期:2024-03-25 出版日期:2024-10-26 发布日期:2024-10-16
通讯作者: *赵元章, E-mail: zhaoyz@ouc.edu.cn
基金资助:
山东省自然科学基金(ZR2019MA072)

Existence and Nonexistence of Solutions for Nonhomogeneous Dirichlet Exterior Problem to a Semilinear Hyperbolic Differential Inequality

Xiao Suping¹,Zhao Yuanzhang^2,^*()

¹School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030000
²School of Mathematical Sciences, Ocean University of China, Shandong Qingdao 266100

Received:2023-10-04 Revised:2024-03-25 Online:2024-10-26 Published:2024-10-16
Supported by:
Natural Science Foundation of Shandong Province of China(ZR2019MA072)

摘要/Abstract

摘要：

该文研究在高维外区域中 ($N\geq2$) 的一类半线性双曲型微分不等式非齐次 Dirichlet 外问题. 利用适当选取试验函数的方法及反证技巧, 在依赖于时空变量的非齐次 Dirichlet 边界条件下建立问题解的非存在性定理且导出一些解的存在性结论.

关键词: 双曲型微分不等式, 非齐次 Dirichlet 外问题, 存在性, 非存在性

Abstract:

This paper is concerned with the nonhomogeneous Dirichlet exterior problem for a semilinear hyperbolic differential inequality in the higher dimensional space ($N\geq2$). Using the test function method and contradiction argument, we establish the nonexistence theorem under the nonhomogeneous Dirichlet boundary condition, which depends both on time and space. Meantime, we obtain some existence results.

Key words: Hyperbolic differential inequality, Nonhomogeneous Dirichlet exterior problem, Existence, Nonexistence

中图分类号:

O175.23

肖苏平, 赵元章. 一类半线性双曲型微分不等式非齐次 Dirichlet 外问题解的存在性与非存在性[J]. 数学物理学报, 2024, 44(5): 1167-1182.

Xiao Suping, Zhao Yuanzhang. Existence and Nonexistence of Solutions for Nonhomogeneous Dirichlet Exterior Problem to a Semilinear Hyperbolic Differential Inequality[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1167-1182.

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