Positive solutions for a class of singular fractional differential equation with infinite-point boundary value conditions
Positive solutions for a class of singular fractional differential equation with infinite-point boundary value conditions
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一类具有无限点边值条件的奇异分数阶微分方程的正解
DOI：
10.1016/j.aml.2014.08.008
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发表时间：
2015
影响因子：
3.7
通讯作者：
Xingqiu Zhang
中科院分区：
文献类型：
--
作者：
Xingqiu Zhang
考虑非线性分数阶微分方程具有无穷点边值条件{D 0+ α u（t）+ q（t）f（t，u（t））= 0，0< t< 1，u（0）= u′（0）= n = u（n− 2）（0）= 0，u（i）（1）=∑ j= 1∞ α ju（n j），其中α> 2，n− 1< α≤ n，i∈[1，n− 2]是一个固定整数，α j≥ 0，0<1<2<<j− 1<j<< 1（j= 1，2，...），Δ−∑ j= 1∞ α j j α− 1> 0，Δ=（α− 1）（α− 2）<$（α− i）。非线性项f允许关于时间和空间变量的奇异性。通过在某些有界集上引入非线性项的高度函数，并考虑这些高度函数的积分，得到了几个局部正解存在性和多解性定理。
We consider the following nonlinear fractional differential equation with infinite-point boundary value conditions {D 0+ α u (t)+ q (t) f (t, u (t))= 0, 0< t< 1, u (0)= u′(0)=⋯= u (n− 2)(0)= 0, u (i)(1)=∑ j= 1∞ α j u (ξ j), where α> 2, n− 1< α≤ n, i∈[1, n− 2] is a fixed integer, α j≥ 0, 0< ξ 1< ξ 2<⋯< ξ j− 1< ξ j<⋯< 1 (j= 1, 2,…), Δ−∑ j= 1∞ α j ξ j α− 1> 0, Δ=(α− 1)(α− 2)⋯(α− i). The nonlinear term f permits singularities with respect to both the time and space variables. By introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions, several local existence and multiplicity of positive solutions theorems are obtained.