Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator
We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation with p-Laplacian operator D0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0, 0<t<1, u(0)=u′(1)=0, u′′(0)=0, D0+αu(t)|t=0=0, where 0<γ<1, 2<α<3, 0...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/495138 |
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| author | Jinhua Wang Hongjun Xiang ZhiGang Liu |
| author_facet | Jinhua Wang Hongjun Xiang ZhiGang Liu |
| author_sort | Jinhua Wang |
| collection | DOAJ |
| description | We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation with p-Laplacian operator D0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0, 0<t<1, u(0)=u′(1)=0, u′′(0)=0, D0+αu(t)|t=0=0, where 0<γ<1, 2<α<3, 0<ρ⩽1, D0+α denotes the Caputo derivative, and f:[0,1]×[0,+∞)×R→[0,+∞) is continuous function, ϕp(s)=|s|p-2s, p>1, (ϕp)-1=ϕq, 1/p+1/q=1. By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works. |
| format | Article |
| id | doaj-art-efe03f530eea4cdd8b797f3b242d032f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-efe03f530eea4cdd8b797f3b242d032f2025-02-03T01:27:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/495138495138Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian OperatorJinhua Wang0Hongjun Xiang1ZhiGang Liu2Department of Mathematics, Xiangnan University, Chenzhou 423000, ChinaDepartment of Mathematics, Xiangnan University, Chenzhou 423000, ChinaDepartment of Mathematics, Xiangnan University, Chenzhou 423000, ChinaWe consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation with p-Laplacian operator D0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0, 0<t<1, u(0)=u′(1)=0, u′′(0)=0, D0+αu(t)|t=0=0, where 0<γ<1, 2<α<3, 0<ρ⩽1, D0+α denotes the Caputo derivative, and f:[0,1]×[0,+∞)×R→[0,+∞) is continuous function, ϕp(s)=|s|p-2s, p>1, (ϕp)-1=ϕq, 1/p+1/q=1. By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works.http://dx.doi.org/10.1155/2010/495138 |
| spellingShingle | Jinhua Wang Hongjun Xiang ZhiGang Liu Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator International Journal of Mathematics and Mathematical Sciences |
| title | Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator |
| title_full | Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator |
| title_fullStr | Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator |
| title_full_unstemmed | Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator |
| title_short | Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator |
| title_sort | existence of concave positive solutions for boundary value problem of nonlinear fractional differential equation with p laplacian operator |
| url | http://dx.doi.org/10.1155/2010/495138 |
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