Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation

摘要

By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equationD0+αu(t)+λa(t)f(t,u(t))=0,  0<t<1,  u(0)=0,  u(1)=Σi=1∞αiu(ξi)are considered, where1<α≤2is a real number,λis a positive parameter,D0+αis the standard Riemann-Liouville differentiation, andξi∈(0,1),αi∈[0,∞)withΣi=1∞αiξiα-1<1,a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,∞),[0,∞)).