Positive Solutions for Second-Order Three-Point Eigenvalue Problems

Abstract EN

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 problem x′′(t)+λf(t,x(t))=0, 0≤t≤1, x(0)=0, x(1)=x(η), where λ is a parameter.

An illustrative example is given to demonstrate the effectiveness of the obtained result.