Positive Solutions for Second-Order Three-Point Eigenvalue Problems

Abstract

With the help of the fixed point index theorem in cones, we get an existence theorem concerning the existence of positive solution for a second-order three-point eigenvalue problemx′′(t)+λf(t,x(t))=0,  0≤t≤1,  x(0)=0,  x(1)=x(η), whereλis a parameter. An illustrative example is given to demonstrate the effectiveness of the obtained result.