具有共振的分数阶微分方程边值问题解的存在性

Existence of solutions for fractional differential equation boundary value problems at resonance

通过选择恰当的Banach空间及其范数,定义合适的投影算子,利用Mawhin重合度理论和分数阶微分以及分数阶积分的性质,在Riemann-Stieltjes积分边界条件下,研究非线性项中含有分数阶导数且具有共振的分数阶(n-1,1)共轭边值问题解的存在性,其中的非线性项可以是不连续的,并给出一个例子说明了主要结论。

By defining appropriate Banach space and norm, giving the appropriate projectors , using the coincidence degree theory due to Mawhin and the properties of fractional derivative and integral, the existence of solutions for fractional （n-1,1） conjugate boundary value problems with the Riemann-Stieltjes integral boundary condition at resnonce is investigagted, where the nonlinear term contains fractional-order derivative and may be noncontinuous . An example is given to illustrate the main results.