A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems
Let T∈ℕ be an integer with T>1, 𝕋:={1,…,T}, 𝕋^:={0,1,…,T+1}. We consider boundary value problems of nonlinear second-order difference equations of the form Δ2u(t−1)+λa(t)f(u(t))...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2009-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2009/671625 |
| _version_ | 1811295504814833664 |
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| author | Ruyun Ma Youji Xu Chenghua Gao |
| author_facet | Ruyun Ma Youji Xu Chenghua Gao |
| author_sort | Ruyun Ma |
| collection | DOAJ |
| description | Let T∈ℕ be an integer with T>1, 𝕋:={1,…,T}, 𝕋^:={0,1,…,T+1}. We consider boundary value problems of nonlinear second-order difference equations of the form Δ2u(t−1)+λa(t)f(u(t))=0, t∈𝕋, u(0)=u(T+1)=0, where a:𝕋→ℝ+, f∈C([0,∞),[0,∞)) and, f(s)>0 for s>0, and f0=f∞=0, f0=lim⁡s→0+f(s)/s, f∞=lim⁡s→+∞f(s)/s. We investigate the global structure of positive solutions by using the Rabinowitz's global bifurcation theorem. |
| first_indexed | 2024-04-13T05:33:29Z |
| format | Article |
| id | doaj.art-f40403813dc14a2ab82a2f2c4028063a |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T05:33:29Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-f40403813dc14a2ab82a2f2c4028063a2022-12-22T03:00:21ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472009-01-01200910.1155/2009/671625A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value ProblemsRuyun MaYouji XuChenghua GaoLet T∈ℕ be an integer with T>1, 𝕋:={1,…,T}, 𝕋^:={0,1,…,T+1}. We consider boundary value problems of nonlinear second-order difference equations of the form Δ2u(t−1)+λa(t)f(u(t))=0, t∈𝕋, u(0)=u(T+1)=0, where a:𝕋→ℝ+, f∈C([0,∞),[0,∞)) and, f(s)>0 for s>0, and f0=f∞=0, f0=lim⁡s→0+f(s)/s, f∞=lim⁡s→+∞f(s)/s. We investigate the global structure of positive solutions by using the Rabinowitz's global bifurcation theorem.http://dx.doi.org/10.1155/2009/671625 |
| spellingShingle | Ruyun Ma Youji Xu Chenghua Gao A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems Advances in Difference Equations |
| title | A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems |
| title_full | A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems |
| title_fullStr | A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems |
| title_full_unstemmed | A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems |
| title_short | A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems |
| title_sort | global description of the positive solutions of sublinear second order discrete boundary value problems |
| url | http://dx.doi.org/10.1155/2009/671625 |
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