FAN Chengtao,LIN Shuang,GE Qi*.Existence of multiple positions solutions for boundary value problems with a coupled system of fractional q -differences on the half-line[J].Journal of Yanbian University,2017,43(04):291-301,326.
一类定义域在半轴上的分数阶q -差分系统边值问题多重正解的存在性
- Title:
- Existence of multiple positions solutions for boundary value problems with a coupled system of fractional q -differences on the half-line
- Keywords:
- fractional q -differences system; half-line; Krasnoselskii fixed point theorem; Leggett-Williams fixed point theorem; multiple positions solutions
- 分类号:
- O175.6
- 文献标志码:
- A
- 摘要:
- 研究了一类定义域在半轴上的分数阶q-差分系统多重正解的存在性.首先分析了格林函数的一些性质,然后分别利用Krasnoselskii不动点定理、Leggett-Williams不动点定理证明了该方程多重正解的存在性.
- Abstract:
- We study the existence of multiple positions solutions for boundary value problems with a coupled system of fractional q -differences on the half-line. Firstly, we analyze some properties of the Green function. Then, the existence of multiple positive solutions of the equation are proved by applying Krasnoselskii fixed point theorem, Leggett-Williams fixed point theorem.
参考文献/References:
[1] Ernst T. q -Bernoulli and q -Euler polynomials, an umbral approach[J]. International Journal of Difference Equations, 2006,1(1):31-80.
[2] Ernst T. q -Pascal and q -Bernoulli matrices, an umbral approach[J]. Advances in Dynamical Systems & Applications, 2008,3(2):251-282.
[3] Agarwal R P. Certain fractional q -integrals and q -derivatives[J]. Proc Cambridge Philos Soc, 1969,66:365-370.
[4] Atici F M, Eloe P W. Fractional q -calculus on a time scale[J]. J Nonlinear Math Phys, 2007,14(3):333-344.
[5] Rajkovic P M, Marinkovic S D, Stankovic M S. Fractional integrals and derivatives in q-calculus[J]. Discrete Math, 2007,1(1):311-323.
[6] 孙明哲,韩筱爽.一类分数阶q-差分边值问题的正解[J].延边大学学报(自然科学版),2013,39(4):252-255.
[7] Ahmad B, Nieto J J, Alsaedi A, et al. Existence of solutions for nonlinear fractional q -difference integral equations with two fractional orders and nonlocal four-point boundary conditions[J]. Journal of the Franklin Institute, 2014,351:2890-2909.
[8] Agarwal R P, Ahmad B, Alsaedi A, et al. Existence theory for q -antiperiodic boundary value problems of sequential q -fractional integro differential equations[J]. Abstract and Applied Analysis, 2014,2014:1-12.
[9] Sitthiwirattham Thanin. On nonlocal fractional q -integral boundary value problems of fractional q-difference and fractional q -integrodifference equations involving different numbers of order and q[J]. Boundary Value Problems, 2016,12:1-19.
[10] Wang G, Ahmad B, Zhang L. A coupled system of nonlinear fractional differential equations with multipoint fractional boundary conditions on an unbounded domain[J]. Abstract and Applied Analysis, 2012,2012:1-11.
[11] Su Xinwei, Zhang Shuqin. Unbounded solutions to a boundary value problem of fractional order on the half-line[J]. Computers and Mathematics with Applications, 2011,61:1079-1087.
[12] Zhao Y L, Chen H B, Zhang Q M. Existence and multiplicity of positive solutions for nonhomogeneous boundary value problems with fractional q -derivatives[J]. Boundary Value Problems, 2013,2013:103.
[13] 葛琦,侯成敏.一类分数阶差分方程边值问题多重正解的存在性[J].东北石油大学学报,2012,36(4):101-110.
备注/Memo
收稿日期: 2017-10-16 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.