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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| Format: | Article |
| Language: | English |
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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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| author | A. Kameswara Rao |
| author_facet | A. Kameswara Rao |
| author_sort | A. Kameswara Rao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ef7c2995f1cd4fff95c61ae9930e8bed |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-ef7c2995f1cd4fff95c61ae9930e8bed2025-02-03T01:31:51ZengWileyInternational Journal of Differential Equations1687-96431687-96512015-01-01201510.1155/2015/567209567209Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of p-Laplacian Dynamic Equations on Time ScalesA. Kameswara Rao0Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Madhurawada, Visakhapatnam 530 048, IndiaWe 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.http://dx.doi.org/10.1155/2015/567209 |
| spellingShingle | A. Kameswara Rao Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of p-Laplacian Dynamic Equations on Time Scales International Journal of Differential Equations |
| title | Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of p-Laplacian Dynamic Equations on Time Scales |
| title_full | Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of p-Laplacian Dynamic Equations on Time Scales |
| title_fullStr | Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of p-Laplacian Dynamic Equations on Time Scales |
| title_full_unstemmed | Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of p-Laplacian Dynamic Equations on Time Scales |
| title_short | Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of p-Laplacian Dynamic Equations on Time Scales |
| title_sort | existence and iteration of positive solutions to third order bvp for a class of p laplacian dynamic equations on time scales |
| url | http://dx.doi.org/10.1155/2015/567209 |
| work_keys_str_mv | AT akameswararao existenceanditerationofpositivesolutionstothirdorderbvpforaclassofplaplaciandynamicequationsontimescales |