一类二阶差分方程组 Robin 边值问题的正解
Positive Solutions of Robin Boundary Value Problems for a Class of Second-Order Difference System
DOI: 10.12677/PM.2022.126102, PDF, HTML,    国家自然科学基金支持
作者: 吴海艺：西北师范大学，数学与统计学院，甘肃 兰州
关键词: Jensen不等式；正解；二阶差分方程组；不动点指数理论；Jensen’s Inequality； Positive Solutions； Second-Order Difference Equations； Fixed Point Index Theory
摘要: 本文出于对差分方程组边值问题非线性项的耦合增长的思考，解决了一类非线性差分方程组边值问题的正解。运用了非负上凸函数的 Jensen 不等式和不动点指数理论讨论了一类二阶差分方程组Robin边值问题正解的存在性，其中T≥2是一个整数，Δu(t)=u(t+1)-u(t)是前向差分算子，f,g:[1,T]ℤ×[0;1)×[0;1)→[0;1)连续。
Abstract: In this paper, we consider the coupled growth of nonlinear terms for boundary value problems of systems of difference equations, resolve the positive solutions of boundary value problems for a class of nonlinear difference equations. Also by using Jensen’s inequality for nonnegative concave functions and the fixed point index theory, we discuss the existence of positive solutions of Robin boundary value problems for a class of second-order difference system where T≥2 is the integer,Δu(t)=u(t+1)-u(t) is the forward difference operator, f,g:[1,T]ℤ×[0;1)×[0;1)→[0;1) are continuous.
文章引用：吴海艺. 一类二阶差分方程组 Robin 边值问题的正解[J]. 理论数学, 2022, 12(6): 928-937. https://doi.org/10.12677/PM.2022.126102

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