Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems
We investigate the existence of multiple positive solutions of fractional differential equations with p-Laplacian operator Da+β(ϕp(Da+αu(t)))=f(t,u(t)), a<t<b, uja=0, j=0,1,2,…,n-2, u(α1)(b)=ξu(α1)(η), ϕp(Da+αu(a))=0=Da+β1(ϕp(Da+αu(b))), where β∈(1,2], α∈(n-1,n], n≥3, ξ∈(0,∞), η∈(a,b), β1∈(...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2016/6906049 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568223358255104 |
|---|---|
| author | Sabbavarapu Nageswara Rao |
| author_facet | Sabbavarapu Nageswara Rao |
| author_sort | Sabbavarapu Nageswara Rao |
| collection | DOAJ |
| description | We investigate the existence of multiple positive solutions of fractional differential equations with p-Laplacian operator Da+β(ϕp(Da+αu(t)))=f(t,u(t)), a<t<b, uja=0, j=0,1,2,…,n-2, u(α1)(b)=ξu(α1)(η), ϕp(Da+αu(a))=0=Da+β1(ϕp(Da+αu(b))), where β∈(1,2], α∈(n-1,n], n≥3, ξ∈(0,∞), η∈(a,b), β1∈(0,1], α1∈{1,2,…,α-2} is a fixed integer, and ϕp(s)=|s|p-2s, p>1, ϕp-1=ϕq, (1/p)+(1/q)=1, by applying Leggett–Williams fixed point theorems and fixed point index theory. |
| format | Article |
| id | doaj-art-7d8446c4ecf349688b42771fb5a55c1d |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-7d8446c4ecf349688b42771fb5a55c1d2025-02-03T00:59:34ZengWileyInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/69060496906049Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value ProblemsSabbavarapu Nageswara Rao0Department of Mathematics, Jazan University, P.O. Box 114, Jazan, Saudi ArabiaWe investigate the existence of multiple positive solutions of fractional differential equations with p-Laplacian operator Da+β(ϕp(Da+αu(t)))=f(t,u(t)), a<t<b, uja=0, j=0,1,2,…,n-2, u(α1)(b)=ξu(α1)(η), ϕp(Da+αu(a))=0=Da+β1(ϕp(Da+αu(b))), where β∈(1,2], α∈(n-1,n], n≥3, ξ∈(0,∞), η∈(a,b), β1∈(0,1], α1∈{1,2,…,α-2} is a fixed integer, and ϕp(s)=|s|p-2s, p>1, ϕp-1=ϕq, (1/p)+(1/q)=1, by applying Leggett–Williams fixed point theorems and fixed point index theory.http://dx.doi.org/10.1155/2016/6906049 |
| spellingShingle | Sabbavarapu Nageswara Rao Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems International Journal of Differential Equations |
| title | Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems |
| title_full | Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems |
| title_fullStr | Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems |
| title_full_unstemmed | Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems |
| title_short | Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems |
| title_sort | multiplicity of positive solutions for fractional differential equation with p laplacian boundary value problems |
| url | http://dx.doi.org/10.1155/2016/6906049 |
| work_keys_str_mv | AT sabbavarapunageswararao multiplicityofpositivesolutionsforfractionaldifferentialequationwithplaplacianboundaryvalueproblems |