Solution to a Semilinear Problem on Type II Regions Determined by the Fucik Spectrum

Abstract

We prove the existence of solutions to the semi-linear problem u'' (x) + ⍺u+(x) + βu-(x) = ƒ(x), x ∈ (0, π), u(0) = u(π) = 0 where the point (⍺, β) falls in regions of type (II) between curves of the Fučík spectrum. We use a variational method based on the generalization of the Saddle Point Theorem.