Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions
By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: −u′′(t)=λ[f(t,u(t))−q(t)], 0<t<1, αu(0)−βu′(0)=∫01u(s)dξ(s), γu(1)+δu′(1)=∫01u(s)dη(s), where λ>0...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/696283 |
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| author | Jiqiang Jiang Lishan Liu Yonghong Wu |
| author_facet | Jiqiang Jiang Lishan Liu Yonghong Wu |
| author_sort | Jiqiang Jiang |
| collection | DOAJ |
| description | By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: −u′′(t)=λ[f(t,u(t))−q(t)], 0<t<1, αu(0)−βu′(0)=∫01u(s)dξ(s), γu(1)+δu′(1)=∫01u(s)dη(s),
where λ>0 is a parameter; f:(0,1)×(0,∞)→[0,∞)
is continuous; f(t,x)
may be singular at t=0, t=1, and x=0, and the perturbed term q:(0,1)→[0,+∞) is Lebesgue integrable and may have finitely many singularities in (0,1), which implies that the nonlinear term may change sign. |
| format | Article |
| id | doaj-art-8413d2a6acb74c4f946ed8af2e9d2e01 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8413d2a6acb74c4f946ed8af2e9d2e012025-02-03T06:11:29ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/696283696283Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral ConditionsJiqiang Jiang0Lishan Liu1Yonghong Wu2School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, ChinaDepartment of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, AustraliaBy means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: −u′′(t)=λ[f(t,u(t))−q(t)], 0<t<1, αu(0)−βu′(0)=∫01u(s)dξ(s), γu(1)+δu′(1)=∫01u(s)dη(s), where λ>0 is a parameter; f:(0,1)×(0,∞)→[0,∞) is continuous; f(t,x) may be singular at t=0, t=1, and x=0, and the perturbed term q:(0,1)→[0,+∞) is Lebesgue integrable and may have finitely many singularities in (0,1), which implies that the nonlinear term may change sign.http://dx.doi.org/10.1155/2012/696283 |
| spellingShingle | Jiqiang Jiang Lishan Liu Yonghong Wu Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions Abstract and Applied Analysis |
| title | Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions |
| title_full | Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions |
| title_fullStr | Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions |
| title_full_unstemmed | Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions |
| title_short | Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions |
| title_sort | positive solutions for second order singular semipositone differential equations involving stieltjes integral conditions |
| url | http://dx.doi.org/10.1155/2012/696283 |
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