Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum
Consider the multiplicity of solutions to the nonlinear second-order discrete problems with minimum and maximum: Δ2u(k−1)=f(k,u(k),Δu(k)), k∈T, min{u(k):k∈T^}=A, maxâ¡{u(k):k∈T^}=B, where f:T×â„Â2→â„Â,  a,b∈ℕ are fixed numbers sat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2008-09-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2008/586020 |
| _version_ | 1819289602715811840 |
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| author | Chenghua Gao Ruyun Ma |
| author_facet | Chenghua Gao Ruyun Ma |
| author_sort | Chenghua Gao |
| collection | DOAJ |
| description | Consider the multiplicity of solutions to the nonlinear second-order discrete problems with minimum and maximum: Δ2u(k−1)=f(k,u(k),Δu(k)), k∈T, min{u(k):k∈T^}=A, maxâ¡{u(k):k∈T^}=B, where f:T×â„Â2→â„Â,  a,b∈ℕ are fixed numbers satisfying b≥a+2,  and  A,B∈℠are satisfying B>A,   T={a+1,…,b−1},  T^={a,a+1,…,b−1,b}. |
| first_indexed | 2024-12-24T03:09:28Z |
| format | Article |
| id | doaj.art-18398c61f220437da15aad40a69dd894 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-24T03:09:28Z |
| publishDate | 2008-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-18398c61f220437da15aad40a69dd8942022-12-21T17:17:51ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472008-09-01200810.1155/2008/586020Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and MaximumChenghua GaoRuyun MaConsider the multiplicity of solutions to the nonlinear second-order discrete problems with minimum and maximum: Δ2u(k−1)=f(k,u(k),Δu(k)), k∈T, min{u(k):k∈T^}=A, maxâ¡{u(k):k∈T^}=B, where f:T×â„Â2→â„Â,  a,b∈ℕ are fixed numbers satisfying b≥a+2,  and  A,B∈℠are satisfying B>A,   T={a+1,…,b−1},  T^={a,a+1,…,b−1,b}.http://dx.doi.org/10.1155/2008/586020 |
| spellingShingle | Chenghua Gao Ruyun Ma Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum Advances in Difference Equations |
| title | Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum |
| title_full | Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum |
| title_fullStr | Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum |
| title_full_unstemmed | Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum |
| title_short | Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum |
| title_sort | existence and multiple solutions for nonlinear second order discrete problems with minimum and maximum |
| url | http://dx.doi.org/10.1155/2008/586020 |
| work_keys_str_mv | AT chenghuagao existenceandmultiplesolutionsfornonlinearsecondorderdiscreteproblemswithminimumandmaximum AT ruyunma existenceandmultiplesolutionsfornonlinearsecondorderdiscreteproblemswithminimumandmaximum |