Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions

The nonlinear nnth-order singular nonlocal boundary value problem {u(n)(t)+λa(t)f(t,u(t))=0,t∈(0,1),u(0)=u′(0)=⋯=u(n−2)(0)=0,u(1)=∫01u(s)dA(s) is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, where ∫01u(s)dA(s) is given by a Riemann–Stieltjes integral with a signed measure, aa may be singular at t=0t=0 and/or t=1,f(t,x) may also have singularity at x=0x=0. The existence of positive solutions is obtained by means of the fixed point index theory in cones.