分数阶微分方程边值问题非平凡解的存在性

Existence of nontrivial solutions for boundary value problems of fractional differential equations

运用Leray-Schauder度理论,在相关算子第一特征值条件下,获得分数阶微分方程边值问题{Dα0+u(t)=-f(t,u(t)),t∈[0,1]u(0)=u'(0)=u'(1)=0非平凡解的存在性,其中α∈(2,3]是一实数,Dα0+是α阶Riemann-Liouville分数阶导数。

By applying the theory of Leray-Schauder degree,the existence of nontrivial solutions for the boundary value problems of fractional differential equations{Dα0 ＋ u（t）=-f（t,u（t））,t∈[0,1] u（0）=u′（0）=u′（1）=0 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator.Hereα∈（2,3]is a real number,Dα0 ＋ is the standard Riemann-Liouville fractional derivative of order α.