带有脉冲的微分方程m点边值问题多重正解
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摘要
将以往所研究的方程的边界条件和脉冲项做了推广,采用锥上不动点定理研究脉冲微分方程m点边值的问题,获得了该问题多重正解的存在性新结果.最后通过具体的实例说明结论的应用.
By using fixed-point theorems in a cones sufficient condition,the author explores the existence result of the multiple positive solutions for a class of second-order impulsive differential equation. The boundary value conditions and impulsive term are extended. Particularly,the new conclusions about the existence of the solution are obtained. At last,the material example shows the application of the results.
By using fixed-point theorems in a cones sufficient condition,the author explores the existence result of the multiple positive solutions for a class of second-order impulsive differential equation. The boundary value conditions and impulsive term are extended. Particularly,the new conclusions about the existence of the solution are obtained. At last,the material example shows the application of the results.
引文
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[2]GEORGE R K,NANDAKUMARAN A K,ARAPOSTATHIS A. A note on controllability of impulsive systems[J]. Journal of Mathematical Analysis and Applications,2000,241(2):276-283.
[3]NENOV S. Impulsive controllability and optimization problems in population dynamics[J]. Nonlinear Analysis,1999,36(7):881-890.
[4]董玉香,王定江.含两种群的非线性森林病虫害模型的定性分析[J].浙江工业大学学报,2010,38(1):71-74.
[5]YANG D,WANG J R,O'REGAN D. A class of nonlinear non-instantaneous impulsive differential equations involving parameters and fractional order[J]. Applied Mathematics&Computation,2018,321:1339-1351.
[6]张海丽.带参数的四阶脉冲微分方程两点边值问题[J].菏泽学院学报,2018,40(2):5-8.
[7]JIANG W H. The existence of positive solutions for second-order multi-point BVPs with the first derivative[J]. Journal of Computational and Applied Mathematics,2009,225(2):387-392.
[8]ZHANG L L,ZHAI C B. Existence and uniqueness of positive solutions to nonlinear second order impulsive differential equations with concave or convex nonlinearities[J]. Discrete Dyn Nat Society,2013,2013:1-11.
[9]魏君,蒋达清,祖力.一维p-Laplace二阶脉冲微分方程的奇异边值问题[J].应用数学学报,2013,36(3):414-430.
[10]李海艳,郭宇恒,李利玫.带有脉冲的二阶多点微分方程的边值问题[J].中北大学学报(自然科学版),2017,38(4):425-432.
[11]陆心怡,张兴秋,王林.一类分数阶微分方程m点边值问题正解的存在性[J].系统科学与数学,2014,34(2):218-230.
[12]李海艳,李振海,李利玫.逆序Banach空间二阶多点边值问题解的存在性和唯一性[J].中国科技论文,2017,12(5):596-600.
[13]李耀红,张晓燕. Banach空间中一类二阶非线性脉冲积分-微分方程边值问题解的存在性[J].应用数学,2011,24(1):112-119.
[14]田景霞.无穷区间上二阶脉冲微分方程多点边值问题的正解[J].应用泛函分析学报,2012,14(3):315-320.
[15]郭大均.非线性泛函分析[M]. 2版.济南:山东科学技术出版社,2001.
[2]GEORGE R K,NANDAKUMARAN A K,ARAPOSTATHIS A. A note on controllability of impulsive systems[J]. Journal of Mathematical Analysis and Applications,2000,241(2):276-283.
[3]NENOV S. Impulsive controllability and optimization problems in population dynamics[J]. Nonlinear Analysis,1999,36(7):881-890.
[4]董玉香,王定江.含两种群的非线性森林病虫害模型的定性分析[J].浙江工业大学学报,2010,38(1):71-74.
[5]YANG D,WANG J R,O'REGAN D. A class of nonlinear non-instantaneous impulsive differential equations involving parameters and fractional order[J]. Applied Mathematics&Computation,2018,321:1339-1351.
[6]张海丽.带参数的四阶脉冲微分方程两点边值问题[J].菏泽学院学报,2018,40(2):5-8.
[7]JIANG W H. The existence of positive solutions for second-order multi-point BVPs with the first derivative[J]. Journal of Computational and Applied Mathematics,2009,225(2):387-392.
[8]ZHANG L L,ZHAI C B. Existence and uniqueness of positive solutions to nonlinear second order impulsive differential equations with concave or convex nonlinearities[J]. Discrete Dyn Nat Society,2013,2013:1-11.
[9]魏君,蒋达清,祖力.一维p-Laplace二阶脉冲微分方程的奇异边值问题[J].应用数学学报,2013,36(3):414-430.
[10]李海艳,郭宇恒,李利玫.带有脉冲的二阶多点微分方程的边值问题[J].中北大学学报(自然科学版),2017,38(4):425-432.
[11]陆心怡,张兴秋,王林.一类分数阶微分方程m点边值问题正解的存在性[J].系统科学与数学,2014,34(2):218-230.
[12]李海艳,李振海,李利玫.逆序Banach空间二阶多点边值问题解的存在性和唯一性[J].中国科技论文,2017,12(5):596-600.
[13]李耀红,张晓燕. Banach空间中一类二阶非线性脉冲积分-微分方程边值问题解的存在性[J].应用数学,2011,24(1):112-119.
[14]田景霞.无穷区间上二阶脉冲微分方程多点边值问题的正解[J].应用泛函分析学报,2012,14(3):315-320.
[15]郭大均.非线性泛函分析[M]. 2版.济南:山东科学技术出版社,2001.