具有超前和滞后的二阶差分方程的边值问题
Boundary Value Problems for Second Order Difference Equations Containing Both Advance and Retardation
DOI: 10.12677/AAM.2016.54081, PDF,    国家自然科学基金支持
作者: 徐佳琳, 周展：广州大学数学与信息科学学院，广东 广州
关键词: 二阶差分方程；边值问题；山路引理；Second Order Difference Equations； Boundary Value Problems； Mountain Pass Lemma
摘要: 本文研究了一类具有超前和滞后的二阶非线性差分方程的边值问题。首先建立边值问题对应的变分泛函，然后将边值问题的解的存在性转化为相应泛函的临界点的存在性，再利用山路引理得到该泛函临界点的存在性，进而得到所求边值问题解的存在性。
Abstract: In this paper, the boundary value problems for a class of second order nonlinear difference equations containing both advance and retardation are studied. First, a variational functional corresponding to the boundary value problems as aforementioned is established. Next, the existence of solutions of the boundary value problems is transformed into the existence of critical points for the corresponding functional. Then, by using Mountain Pass Lemma, the existence of critical points of the functional is obtained, and thus the existence of solutions for the initial boundary value problems is also obtained.
文章引用：徐佳琳, 周展. 具有超前和滞后的二阶差分方程的边值问题[J]. 应用数学进展, 2016, 5(4): 695-704. https://dx.doi.org/10.12677/AAM.2016.54081

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