Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator
We obtain some existence results of solutions for discrete periodic boundary value problems with singular ϕ-Laplacian operator ∇Δuk/1-κ(Δuk)2+rkuk+mk/(uk)λ=ek, 2≤k≤N-1, u1=uN, and Δu1=ΔuN-1 by using the upper and lower solutions method and Brouwer degree theory, where κ>0 is a con...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/637242 |
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| _version_ | 1832564703026479104 |
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| author | Ruyun Ma Yanqiong Lu |
| author_facet | Ruyun Ma Yanqiong Lu |
| author_sort | Ruyun Ma |
| collection | DOAJ |
| description | We obtain some existence results of solutions for discrete periodic boundary value problems with singular ϕ-Laplacian operator ∇Δuk/1-κ(Δuk)2+rkuk+mk/(uk)λ=ek, 2≤k≤N-1, u1=uN, and Δu1=ΔuN-1 by using the upper and lower solutions method and Brouwer degree theory, where κ>0 is a constant, r=(r2,…,rN-1), m=(m2,…,mN-1), e=(e2,…,eN-1)∈RN-2, and λ>0 is a parameter. We also give some examples with singular nonlinearities to illustrate our main results. |
| format | Article |
| id | doaj-art-a8d58844c32149c9baa57ecfbf498f9c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a8d58844c32149c9baa57ecfbf498f9c2025-02-03T01:10:30ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/637242637242Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian OperatorRuyun Ma0Yanqiong Lu1Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe obtain some existence results of solutions for discrete periodic boundary value problems with singular ϕ-Laplacian operator ∇Δuk/1-κ(Δuk)2+rkuk+mk/(uk)λ=ek, 2≤k≤N-1, u1=uN, and Δu1=ΔuN-1 by using the upper and lower solutions method and Brouwer degree theory, where κ>0 is a constant, r=(r2,…,rN-1), m=(m2,…,mN-1), e=(e2,…,eN-1)∈RN-2, and λ>0 is a parameter. We also give some examples with singular nonlinearities to illustrate our main results.http://dx.doi.org/10.1155/2014/637242 |
| spellingShingle | Ruyun Ma Yanqiong Lu Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator Discrete Dynamics in Nature and Society |
| title | Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator |
| title_full | Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator |
| title_fullStr | Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator |
| title_full_unstemmed | Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator |
| title_short | Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator |
| title_sort | periodic solutions of second order nonlinear difference equations with singular ϕ laplacian operator |
| url | http://dx.doi.org/10.1155/2014/637242 |
| work_keys_str_mv | AT ruyunma periodicsolutionsofsecondordernonlineardifferenceequationswithsingularphlaplacianoperator AT yanqionglu periodicsolutionsofsecondordernonlineardifferenceequationswithsingularphlaplacianoperator |