TY - JOUR
A2 - Xie, Fuding
AU - Ren, Teng
AU - Chen, Xiaochun
PY - 2013
DA - 2013/03/28
TI - Positive Solutions of Fractional Differential Equation with -Laplacian Operator
SP - 789836
VL - 2013
AB - The basic assumption of ecological economics is that resource allocation exists social optimalsolution, 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 ofecological economics. In this paper, we study an ecological model arising from ecological economics bymathematical method, that is, study the existence of positive solutions for the fractional differential equationwith p-Laplacian operator Dtβ(φp(Dtαx))(t)=f(t,x(t)), t∈(0,1), x(0)=0, x(1)=ax(ξ), Dtαx(0)=0, and Dtαx1=bDtαxη, where Dtα,Dtβ are the standard Riemann-Liouville derivatives, p-Laplacian operator is defined as φps=sp-2s,p>1, and the nonlinearity f may be singular at both t=0,1 and x=0. By finding moresuitable upper and lower solutions, we omit some key conditions of some existing works, and the existenceof positive solution is established.
SN - 1085-3375
UR - https://doi.org/10.1155/2013/789836
DO - 10.1155/2013/789836
JF - Abstract and Applied Analysis
PB - Hindawi Publishing Corporation
KW -
ER -