FAN Chengtao,GE Qi*.Existence of multiple positions solutions for a class of fractional q-differences equation with fractional boundary value conditions[J].Journal of Yanbian University,2016,42(04):289-296,324.
一类带有分数阶边值条件的分数阶q-差分方程多重正解的存在性
- Title:
- Existence of multiple positions solutions for a class of fractional q-differences equation with fractional boundary value conditions
- Keywords:
- fractional q-differences; 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:
- 研究一类带有分数阶差分边值条件的分数阶q-差分方程多重正解的存在性.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不动点定理和对推广了的Krasnoselskii不动点定理证明了该方程多重正解的存在性.
- Abstract:
- This paper is devoted to existence of multiple positive solutions for a class of the fractional q-differences equation with the fractional q-differences boundary conditions. Firstly, we analyze some properties of the Green function. The second, the existence of multiple positive solutions of the equation are proved by applying Krasnoselskii fixed point theorem, Leggett -Williams fixed point theorem, and a new extension of Krasnoselskii fixed point theorem.
参考文献/References:
[1] Ernst T. Some results for q-functions of many variables[M]. Rend Padova, 2004.
[2] Ernst T. q-Bernoulli and q-Euler polynomials, an umbral approach[J]. Int J Difference Equations, 2006,51(1):31-80.[3] Yang W G. Positive solutions for nonlinear semipositone fractional q-difference system with coupled integral boundary conditions[J]. Applied Mathematics and Computation, 2014,244:702-725.
[4] Ricardo A, Natalia M. Existence results for fractional q-difference equations of order [2,3] with three-point boundary conditions[J]. Commun Nonlinear Sci Numer Simulat, 2014,19:1675-1685.
[5] Jiang M, Zhong S. Existence of solutions for nonlinear fractional q-difference equations with Riemann-Liouville type q-derivatives[J]. Applied Mathematics and Computation, 2015,47:429-459.
[6] Li X H, Han Z L, Zhao Y. Existence and multiplicity of positives solutions for fractional q-difference equations with parameter[J]. International Journal of Dynamical Systems and Differential Equations, 2015,5(4):267-287.
[7] 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.
[8] 葛琦,侯成敏.一类分数阶q-差分边值问题的多重正解的存在性[J].黑龙江大学自然科学学报,2015,32(2):163-170.
[9] 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.
[10] 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.
[11] Guo Y, Ge W. Positive solutions for three-point boundary value problems with dependence on the first order derivative[J]. Journal of Mathematical Analysis and Applications, 2004,209(1):291-301.
相似文献/References:
[1]孙明哲,侯成敏.一类分数阶q-差分系统边值问题解的存在性[J].延边大学学报(自然科学版),2015,41(01):10.
SUN Mingzhe,HOU Chengmin.Existence of solutions for boundary value problems with a coupled system of fractional q -differences[J].Journal of Yanbian University,2015,41(04):10.
[2]苏巍,刘畅,李丹,等.一类分数阶q -差分方程边值问题正解的存在性[J].延边大学学报(自然科学版),2015,41(02):103.
SU Wei,LIU Chang,LI Dan,et al.Existence of positive solutions for a class of the boundary value problems of fractional q-difference equations[J].Journal of Yanbian University,2015,41(04):103.
[3]范成涛,葛琦.一类带有分数阶边值条件的分数阶q-差分方程解的存在性[J].延边大学学报(自然科学版),2015,41(03):207.
FAN Chengtao,GE Qi*.Existence of solutions for a class of fractional q-differences equation with fractional boundary value conditions[J].Journal of Yanbian University,2015,41(04):207.
[4]范成涛,林爽,葛琦*.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[J].延边大学学报(自然科学版),2017,43(04):291.
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.
备注/Memo
收稿日期: 2016-11-16 *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.
基金项目: 国家自然科学基金资助项目(11161049); 吉林省教育厅“十二五”科技项目(吉教科合字[2015]第36号)