From the introduction and summary: In this paper, we are concerned with positive solutions for singular \((k,n-k)\) conjugate boundary value problem \[ (-1)^{n-k} y^{(n)}(x)=\lambda h(x) f(y),\qquad 0<x<1, \]
\[ y^{(i)}(0)= ,\;y^{(j)}(1)= 0,\qquad 0\leq i\leq k-1,\;0\leq j\leq n-k-1, \] where \(1\leq k\leq n-1\) is a positive number and \(\lambda>0\) is a parameter.
The existence of a positive solution is studied by employing a priori estimates, the conce theorem and the fixed index.