Solvability for two-point boundary value problems

Abstract

To prove the solvability problem of -u″ = u + g(u) - h(x), u(0) = u(π) = 0 where h ∈ L2(0, π) and g ∈ C(R,R), a known sufficient condition such as Landesman-Laser condition with the Saddle Point theorem can be used.