Necessary and sufficient conditions for the existence of solution to three-point BVP Original Research Article

We study the existence of a solution of the three-point boundary value problem equation(P) View the MathML sourcex″+λx+g(x)=h,x(0)=0,x(η)=x(π). Turn MathJax on We give sufficient and necessary conditions on gg and hh in order for (P) to have a real solution. Our conditions are of Landesman–Lazer type and depend on the real values of λλ and ηη.