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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |