Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales
We study a system of second-order dynamic equations on time scales (p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t), u2(t))=0, satisfying four kinds of different multipoint boundary value conditions, fi is continuous and semipositone. We derive an interval of...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/679316 |
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| author | Gang Wu Longsuo Li Xinrong Cong Xiufeng Miao |
| author_facet | Gang Wu Longsuo Li Xinrong Cong Xiufeng Miao |
| author_sort | Gang Wu |
| collection | DOAJ |
| description | We study a system of second-order dynamic equations on time scales (p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t), u2(t))=0, satisfying four kinds of different multipoint boundary value conditions, fi is continuous and semipositone. We derive an interval of λ such that any λ lying in this interval, the semipositone coupled boundary value problem has multiple positive solutions. The arguments are based upon fixed-point theorems in a cone. |
| format | Article |
| id | doaj-art-b1c127454d4347488f5d669df8cd86df |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b1c127454d4347488f5d669df8cd86df2025-02-03T00:59:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/679316679316Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time ScalesGang Wu0Longsuo Li1Xinrong Cong2Xiufeng Miao3Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, ChinaWe study a system of second-order dynamic equations on time scales (p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t), u2(t))=0, satisfying four kinds of different multipoint boundary value conditions, fi is continuous and semipositone. We derive an interval of λ such that any λ lying in this interval, the semipositone coupled boundary value problem has multiple positive solutions. The arguments are based upon fixed-point theorems in a cone.http://dx.doi.org/10.1155/2013/679316 |
| spellingShingle | Gang Wu Longsuo Li Xinrong Cong Xiufeng Miao Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales Journal of Applied Mathematics |
| title | Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales |
| title_full | Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales |
| title_fullStr | Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales |
| title_full_unstemmed | Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales |
| title_short | Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales |
| title_sort | multiple positive solutions to multipoint boundary value problem for a system of second order nonlinear semipositone differential equations on time scales |
| url | http://dx.doi.org/10.1155/2013/679316 |
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