Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales
We study a general second-order m-point boundary value problems for nonlinear singular impulsive dynamic equations on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+q(t)f(t,u(t))=0,t∈(0,1),t≠tk,uΔ(tk+)=uΔ(tk)-Ik(u(tk)), and k=1,2,…,n,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi). The existence and uniqueness of positive...
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| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/867018 |
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| author | Xue Xu Yong Wang |
| author_facet | Xue Xu Yong Wang |
| author_sort | Xue Xu |
| collection | DOAJ |
| description | We study a general second-order m-point boundary value problems for nonlinear singular impulsive dynamic equations on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+q(t)f(t,u(t))=0,t∈(0,1),t≠tk,uΔ(tk+)=uΔ(tk)-Ik(u(tk)), and k=1,2,…,n,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi). The existence and uniqueness of positive solutions are established by using the mixed monotone fixed point theorem on cone and Krasnosel’skii fixed point theorem. In this paper, the function items may be singular in its dependent variable. We present examples to illustrate our results. |
| format | Article |
| id | doaj-art-13e9198a97a14d2cb5ebf4ec5f30a14f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-13e9198a97a14d2cb5ebf4ec5f30a14f2025-02-03T01:09:07ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/867018867018Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time ScalesXue Xu0Yong Wang1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaWe study a general second-order m-point boundary value problems for nonlinear singular impulsive dynamic equations on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+q(t)f(t,u(t))=0,t∈(0,1),t≠tk,uΔ(tk+)=uΔ(tk)-Ik(u(tk)), and k=1,2,…,n,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi). The existence and uniqueness of positive solutions are established by using the mixed monotone fixed point theorem on cone and Krasnosel’skii fixed point theorem. In this paper, the function items may be singular in its dependent variable. We present examples to illustrate our results.http://dx.doi.org/10.1155/2014/867018 |
| spellingShingle | Xue Xu Yong Wang Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales Journal of Applied Mathematics |
| title | Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales |
| title_full | Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales |
| title_fullStr | Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales |
| title_full_unstemmed | Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales |
| title_short | Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales |
| title_sort | solutions of second order m point boundary value problems for impulsive dynamic equations on time scales |
| url | http://dx.doi.org/10.1155/2014/867018 |
| work_keys_str_mv | AT xuexu solutionsofsecondordermpointboundaryvalueproblemsforimpulsivedynamicequationsontimescales AT yongwang solutionsofsecondordermpointboundaryvalueproblemsforimpulsivedynamicequationsontimescales |