[1]李宝玲,葛琦*.一类带有p -Laplacian算子的分数阶差分方程的多重解[J].延边大学学报(自然科学版),2014,40(02):104-108.
　LI Baoling,GE Qi*.Multiple solutions for a class of fractional difference equations involving the p -Laplacian operator[J].Journal of Yanbian University,2014,40(02):104-108.
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一类带有p -Laplacian算子的分数阶差分方程的多重解

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第40卷 期数: 2014年02期 页码: 104-108 栏目: 基础科学研究 出版日期: 2014-06-20
Title:
Multiple solutions for a class of fractional difference equations involving the p -Laplacian operator
作者:
李宝玲;  葛琦*
延边大学理学院 数学系, 吉林 延吉 133002
Author(s):
LI Baoling;  GE Qi*
Department of Mathematics, College of Science, Yanbian University, Yanji 133002, China
关键词:
p -Laplacian算子;  变分法;  临界点定理;  多重解
Keywords:
p-Laplacian operator;  variational methods;  the critical points theorem;  multiple solutions
分类号:
O175.7
文献标志码:
A
摘要:
研究了一类带有p -Laplacian算子并依赖于正参数λ的分数阶差分方程的边值问题.利用变分法和带有强制条件的临界点定理,得到了当正参数λ属于某个确定区间时该边值问题至少有3个解的结果.
Abstract:
We studied a class of fractional difference equations with boundary value conditions involving the p -Laplacian operator and depending on a positive real parameter λ. By using variational methods and the critical points theorem with coercive condition, the existence theorem of at least three solutions for this fractional boundary value problem is obtained when the positive parameter λ belongs to some determined interval.

参考文献/References:

[1] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations[M]. Amsterdam: Elsevier, 2006.
[2] Podlubny I. Fractional Differential Equations[M]. San Diego, CA: Academic Press, 1999.
[3] Atici F M, Eloe P W. Two-point boundary value problems for finite fractional difference equations[J]. Difference Equations Applications, 2010,17(4):445-456.
[4] Goodrich C S. Solutions to a discrete right-focal fractional boundary value problem[J]. Difference Equations, 2010,5(2):195-216.
[5] Goodrich C S. On discrete sequential fractional boundary value problem[J]. J Math Anal Appl, 2012,385:111-124.
[6] Atici F M, Eloe P W. A transform method in discrete fractional calculus[J]. Int J Difference Equ, 2007,2(2):165-176.
[7] Atici F M, Sevgi Sengül. Modeling with fractional difference equations[J]. J Math Anal Appl, 2010,369:1-9.
[8] He Yansheng, Hou Chengmin. Existence of solutions for discrete fractional boundary value problems with p -Laplacian operator[J]. Journal of Mathematical Research with Applications, 2014,34(2):197-208.
[9] Frank Ayres. Schaum’s Outline of Theory and Problems of Matrices[M]. New York: Schaum, 1962:134.
[10] Pasquale Candito, Nicola Giovannelli. Multiple solutions for a discrete boundary value problem involving the p-Laplacian[J]. Computers and Mathematics with Applications, 2008,56:959-964.

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备注/Memo

收稿日期: 2013-12-27 基金项目: 国家自然科学基金资助项目(11161049)*通信作者: 葛琦(1975—),女,副教授,研究方向为微分方程理论及应用.

更新日期/Last Update: 2014-06-20