Positive Solutions of Fractional Differential Equation with -Laplacian Operator
The basic assumption of ecological economics is that resource allocation exists social optimal solution, and the social optimal solution and the optimal solution of enterprises can be complementary. The mathematical methods and the ecological model are one of the important means in the study of eco...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/789836 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832555922298241024 |
|---|---|
| author | Teng Ren Xiaochun Chen |
| author_facet | Teng Ren Xiaochun Chen |
| author_sort | Teng Ren |
| collection | DOAJ |
| description | The basic assumption of ecological economics is that resource allocation exists social optimal
solution, and the social optimal solution and the optimal solution of enterprises can be complementary.
The mathematical methods and the ecological model are one of the important means in the study of
ecological economics. In this paper, we study an ecological model arising from ecological economics by
mathematical method, that is, study the existence of positive solutions for the fractional differential equation
with -Laplacian operator , , , , , and , where are the standard Riemann-Liouville derivatives, -Laplacian operator is defined as , and the nonlinearity may be singular at both and By finding more
suitable upper and lower solutions, we omit some key conditions of some existing works, and the existence
of positive solution is established. |
| format | Article |
| id | doaj-art-631101157cd745df857669a31193ecb0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-631101157cd745df857669a31193ecb02025-02-03T05:46:44ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/789836789836Positive Solutions of Fractional Differential Equation with -Laplacian OperatorTeng Ren0Xiaochun Chen1College of Business Administration, Hunan University, Changsha, Hunan 410082, ChinaCollege of Business Administration, Hunan University, Changsha, Hunan 410082, ChinaThe basic assumption of ecological economics is that resource allocation exists social optimal solution, and the social optimal solution and the optimal solution of enterprises can be complementary. The mathematical methods and the ecological model are one of the important means in the study of ecological economics. In this paper, we study an ecological model arising from ecological economics by mathematical method, that is, study the existence of positive solutions for the fractional differential equation with -Laplacian operator , , , , , and , where are the standard Riemann-Liouville derivatives, -Laplacian operator is defined as , and the nonlinearity may be singular at both and By finding more suitable upper and lower solutions, we omit some key conditions of some existing works, and the existence of positive solution is established.http://dx.doi.org/10.1155/2013/789836 |
| spellingShingle | Teng Ren Xiaochun Chen Positive Solutions of Fractional Differential Equation with -Laplacian Operator Abstract and Applied Analysis |
| title | Positive Solutions of Fractional Differential Equation with -Laplacian Operator |
| title_full | Positive Solutions of Fractional Differential Equation with -Laplacian Operator |
| title_fullStr | Positive Solutions of Fractional Differential Equation with -Laplacian Operator |
| title_full_unstemmed | Positive Solutions of Fractional Differential Equation with -Laplacian Operator |
| title_short | Positive Solutions of Fractional Differential Equation with -Laplacian Operator |
| title_sort | positive solutions of fractional differential equation with laplacian operator |
| url | http://dx.doi.org/10.1155/2013/789836 |
| work_keys_str_mv | AT tengren positivesolutionsoffractionaldifferentialequationwithlaplacianoperator AT xiaochunchen positivesolutionsoffractionaldifferentialequationwithlaplacianoperator |