作者机构：
[Xiao, Juan] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Peoples R China.;[Qiu, De-hua] Guangdong Univ Finance & Econ, Sch Math & Stat, Guangzhou 510320, Peoples R China.
通讯机构：
[Qiu, De-hua] G;Guangdong Univ Finance & Econ, Sch Math & Stat, Guangzhou 510320, Peoples R China.
关键词：
pairwise negative quadrant dependent (PNQD) random variable;strong law of large numbers;complete convergence;general moment condition
摘要：
Let {X, X-n,n >= 1} be a sequence of identically distributed pairwise negative quadrant dependent (PNQD) random variables and {a(n),n >= 1} be a sequence of positive constants witha(n)=f(n) andf(theta(k))/f(theta(k-1)) >=beta for all large positive integersk, where 1 <theta <=beta andf(x) > 0 (x >= 1) is a non-decreasing function on [b, +infinity) for someb >= 1. In this paper, we obtain the strong law of large numbers and complete convergence for the sequence {X, X-n,n >= 1}, which are equivalent to the general moment condition n-ary sumation Sigma P-infinity(n=1)(vertical bar X vertical bar>a(n))<infinity. Our results extend and improve the related known works in Baum and Katz [1], Chen at al. [3], and Sung [14].
作者机构：
[胡立军] College of Mathematics and Statistics, Hengyang Normal University, Hengyang, Hunan, 421002, China;[袁礼] Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China;[Zhai J.] Dawning Information Industry Co., Ltd., Beijing, 100193, China
作者机构：
[Deng, Yi-Hua] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.
通讯机构：
[Deng, Yi-Hua] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.
关键词：
p-Laplace equation;variational methods;infinitely many solutions;nonnegative solution
摘要：
In this paper, we study a class of p-Laplace equations. Using variational methods, we prove that there are two solutions and one of these solutions is nonnegative. Using recurrence method, we prove that there are infinitely many solutions to this class of equations.
作者机构：
[张国辉] College of Mathematics and Statistics, Hengyang Normal University, Hengyang, 421008, China;[陈亮陆] Department of Statistics, Ji'nan University, Guangzhou, 510630, China;[陈平炎] Department of Mathematics, Ji'nan University, Guangzhou, 510630, China
作者机构：
衡阳师范学院数学与统计学院, 衡阳, 421008;Indian Statistical Institute(ISI),Chennai Centre, India, Chennai, 600113;[陈少林; 刘刚] 衡阳师范学院数学与统计学院, 衡阳, 421008;[Saminathan Ponnusamy] Indian Statistical Institute(ISI),Chennai Centre, India, Chennai, 600113
作者机构：
[黄海午] College of Mathematics and Statistics,Hengyang Normal University, Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang, 421002
