Positive Solutions of Three-Order Delayed Periodic Boundary Value Problems
Our main purpose is to consider the existence of positive solutions for three-order two-point boundary value problem in the following form: u′′′(t)+ρ3u(t)=f(t,u(t-τ)), 0≤t≤2π, u(i)(0)=u(i)(2π), i=1,2, u(t)=σ, -τ≤t≤0, where σ,ρ, and τ are given constants satisfying τ∈(0,π/2). Some inequality con...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/4143267 |
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| Summary: | Our main purpose is to consider the existence of positive solutions for three-order two-point boundary value problem in the following form: u′′′(t)+ρ3u(t)=f(t,u(t-τ)), 0≤t≤2π, u(i)(0)=u(i)(2π), i=1,2, u(t)=σ, -τ≤t≤0, where σ,ρ, and τ are given constants satisfying τ∈(0,π/2). Some inequality conditions on ρ3u-f(t,u) guaranteeing the existence and nonexistence of positive solutions are presented. Our discussion is based on the fixed point theorem in cones. |
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| ISSN: | 1026-0226 1607-887X |