Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems
By using Morse theory, the critical point theory, and the character of 𝐾1/2, we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem −Δ2𝑥(𝑘−1)=𝑓(𝑘,𝑥(𝑘)),𝑘∈ℤ(1,𝑇) subject to 𝑥(0)=0=Δ𝑥(𝑇), where 𝑇 is a positive integer, ℤ(1,𝑇...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/319829 |
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| author | Jianmin Guo Caixia Guo |
| author_facet | Jianmin Guo Caixia Guo |
| author_sort | Jianmin Guo |
| collection | DOAJ |
| description | By using Morse theory, the critical point theory, and the character
of 𝐾1/2, we consider the existence and multiplicity results of solutions to the following discrete
nonlinear two-point boundary value problem −Δ2𝑥(𝑘−1)=𝑓(𝑘,𝑥(𝑘)),𝑘∈ℤ(1,𝑇) subject to 𝑥(0)=0=Δ𝑥(𝑇), where 𝑇 is a positive integer, ℤ(1,𝑇)={1,2,…,𝑇},Δ is the forward difference operator defined by Δ𝑥(𝑘)=𝑥(𝑘+1)−𝑥(𝑘), and 𝑓∶ℤ(1,𝑇)×ℝ→ℝ is continuous. In argument, Morse inequalities play an important role. |
| format | Article |
| id | doaj-art-c70512954a86445db29a955165deddd5 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-c70512954a86445db29a955165deddd52025-02-03T01:21:56ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/319829319829Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value ProblemsJianmin Guo0Caixia Guo1School of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037008, ChinaSchool of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037008, ChinaBy using Morse theory, the critical point theory, and the character of 𝐾1/2, we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem −Δ2𝑥(𝑘−1)=𝑓(𝑘,𝑥(𝑘)),𝑘∈ℤ(1,𝑇) subject to 𝑥(0)=0=Δ𝑥(𝑇), where 𝑇 is a positive integer, ℤ(1,𝑇)={1,2,…,𝑇},Δ is the forward difference operator defined by Δ𝑥(𝑘)=𝑥(𝑘+1)−𝑥(𝑘), and 𝑓∶ℤ(1,𝑇)×ℝ→ℝ is continuous. In argument, Morse inequalities play an important role.http://dx.doi.org/10.1155/2011/319829 |
| spellingShingle | Jianmin Guo Caixia Guo Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems Discrete Dynamics in Nature and Society |
| title | Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems |
| title_full | Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems |
| title_fullStr | Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems |
| title_full_unstemmed | Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems |
| title_short | Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems |
| title_sort | existence and multiplicity of solutions for discrete nonlinear two point boundary value problems |
| url | http://dx.doi.org/10.1155/2011/319829 |
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