Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of p-Laplacian Dynamic Equations on Time Scales
We investigate the existence and iteration of positive solutions for the following third-order p-Laplacian dynamic equations on time scales: (ϕp(uΔΔ(t)))∇+q(t)f(t,u(t),uΔΔ(t))=0, t∈[a,b],αu(ρ(a))-βuΔ(ρ(a))=0, γu(b)+δuΔ(b)=0, uΔΔ(ρ(a))=0, where ϕp(s) is p-Laplacian operator; that is, ϕp(s)=sp-2s, ...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/567209 |
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| Summary: | We investigate the existence and iteration of positive solutions for the following third-order p-Laplacian dynamic equations on time scales: (ϕp(uΔΔ(t)))∇+q(t)f(t,u(t),uΔΔ(t))=0, t∈[a,b],αu(ρ(a))-βuΔ(ρ(a))=0, γu(b)+δuΔ(b)=0, uΔΔ(ρ(a))=0, where ϕp(s) is p-Laplacian operator; that is, ϕp(s)=sp-2s, p>1, ϕp-1=ϕq, and 1/p+1/q=1. By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problem, but also establish iterative schemes for approximating the solutions. |
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| ISSN: | 1687-9643 1687-9651 |