含超前与滞后量的2n阶p-Laplace差分方程边值问题.doc

含超前与滞后量的 2n 阶 p-Laplace 差分方程
边值问题
周展,王倩
广州大学数学与信息科学学院,广州 510006
广州大学数学与交叉科学广东普通高校重点实验室,广州 510006
摘要:本文考虑含超前与滞后量的 2n 阶 p- Laplace 差分方程边值问题。利用临界点理论,得
到了边值问题解的存在性的一些充分条件。结果推广和改进了最近文献的相关结论。
关键词:边值问题; p-Laplace 差分方程; 2n 阶; 临界点理论.
中图分类号:
Boundary value problems for 2n-order
p-Laplacian difference equations containing both
advance and retardation
ZHOU Zhan, WANG Qian
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006
Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher
Education Institutes, Guangzhou University, Guangzhou 510006
Abstract: In this paper, we consider the boundary value problems for 2n-order p-Laplacian
difference equation containing both advance and retardation. By using critical point theory,
sufficient conditions of the existence of solutions of the boundary value problems are obtained.
Our results generalize and improve some recent ones.
Key words: Boundary value problem; p-Laplacian difference equation; 2n-order; Critical
point theory.
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Introduction
Let N, Z and R denote the sets of all natural numbers, integers and real numbers, re-
spectively. For a, b ∈ Z, define Z(a) = {a, a + 1, · · · }, and Z(a, b) = {a, a + 1, · · · , b} when
a ≤ b.
基金项目: The Specialized Fund for the Doctoral Program of Higher Education of China (no. 201**********) and
Changjiang Scholars and Inno