共振条件下p-Laplacian方程三点边值问题的可解性  

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

作　　者：段磊 陈天兰 DUAN Lei;CHEN Tianlan(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《工程数学学报》2022年第3期502-510,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11801453)。

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。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 threepoint 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.

关 键 词：P-LAPLACIAN算子 共振 连通性 常序上下解 

分 类 号：O175.8[理学—数学]