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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (3): 502-510.doi: 10.3969/j.issn.1005-3085.2022.03.014

• • 上一篇    

共振条件下 $p$-Laplacian 方程三点边值问题的可解性

段   磊,   陈天兰   

  1. 西北师范大学数学与统计学院，兰州 730070
  • 出版日期:2022-06-15 发布日期:2022-08-15
  • 通讯作者: 陈天兰 E-mail: chentianlan511@126.com
  • 基金资助:
    国家自然科学基金 (11801453).

Solvability of Three-point Boundary Value Problems for $p$-Laplacian Equation under Resonant Conditions

DUAN Lei,  CHEN Tianlan   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070
  • Online:2022-06-15 Published:2022-08-15
  • Contact: T. Chen. E-mail address: chentianlan511@126.com
  • Supported by:
    The National Natural Science Foundation of China (11801453).

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摘要：

运用紧向量场方程的解集连通理论和常序上下解方法，对共振条件下 $p$-Laplacian 方程三点边值问题进行了研究，其中的非线性项连续，将所研究的问题改写成定义在某个 Banach 空间上的泛函方程，继而获得解的存在性结果。

关键词: $p$-Laplacian 算子, 共振, 连通性, 常序上下解

Abstract:

By using the solution set connectivity theory of the compact vector field equation and the method of well-ordered upper and lower solutions, studied in this paper is the three-point boundary value problem of $p$-Laplacian equation with the nonlinear term being continuous under resonant conditions. The problem is rewritten as a functional equation defined on Banach space, and the existence of solutions is obtained.

Key words: $p$-Laplacian operator, resonance, connectivity, well-ordered upper and lower solutions

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