Existence of multiple positive solutions of a nonlinear arbitrary order boundary value problem with advanced arguments
Existence of multiple positive solutions of a nonlinear arbitrary order boundary value problem with advanced arguments
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DOI：
10.14232/ejqtde.2012.1.15
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发表时间：
2012
影响因子：
1.1
通讯作者：
Guotao Wang;Lihong Zhang;S. Ntouyas
中科院分区：
文献类型：
--
作者：
Guotao Wang;Lihong Zhang;S. Ntouyas
本文研究了具有超前变元的任意阶非线性分数阶微分方程：D 0+u（t）+ a（t）f（u（θ（t）= 0，0 3（n ∈ N），D 0+是α阶标准Riemann-Liouville分数阶导数，f：[0，∞）→ [0，∞），a：[0，1] →（0，∞），θ：（0，1）→（0，1）是连续函数。利用不动点指数理论和Leggett-Williams不动点定理，建立了上述边值问题存在多个正解的充分条件.
In this paper, we investigate nonlinear fractional differential equations of arbitrary order with advanced arguments D 0+u(t) + a(t)f(u(θ(t))) = 0, 0 3 (n ∈ N), D 0+ is the standard Riemann-Liouville fractional derivative of order α, f : [0,∞) → [0,∞), a : [0, 1] → (0,∞) and θ : (0, 1) → (0, 1] are continuous functions. By applying fixed point index theory and Leggett-Williams fixed point theorem, sufficient conditions for the existence of multiple positive solutions to the above boundary value problem are established.