摘要
研究了一类非线性分数阶时滞微分方程L(D)[x(t)-x(0)]=f(t,xt),x(t)=φ(t)≥0,0t∈<[t-≤r,T0],正解的存在性和惟一性.在f(t,.)非减的条件下,通过运用上下解的方法,获得了该方程正解存在的充分条件,并利用Banach不动点定理证明了该方程正解的惟一性.
The existence and uniqueness of positive solutions for a class of nonlinear fractional differential equation with delay
{L(D)[x(t)-x(0)3-f(t,xl),0〈t≤T,
x(t)=9(t)≥0,t∈[-r,0]
is investigated. By using the sub and super-solution method, some suffcient conditions for its existence of positive solutions are obtained under the condition that f(t, ~ ) is nondecreasing, and the uniqueness of a positive solution is showed by application of the Banach fixed point theorem.
出处
《纺织高校基础科学学报》
CAS
2008年第4期415-420,共6页
Basic Sciences Journal of Textile Universities