Positive solutions for second-order three-point eigenvalue problems (Q1957561)

Summary: By means of the fixed point index theorem in cones, we get an existence theorem concerning the existence of a positive solution for the second-order three-point eigenvalue problem \[ x''(t)+\lambda f(t,x(t))=0,\quad 0\leq t\leq 1,\;x(0)=0,\;x(1)=x(\eta), \] where \(\lambda\) is a parameter. An illustrative example is given to demonstrate the effectiveness of the obtained result.