A three critical point theorem and its applications to the ordinary Dirichlet problem, Topol. Methods Nonlinear Anal

Abstract. The aim of this paper is twofold. On one hand we establish a three critical points theorem for functionals depending on a real parameter λ ∈ Λ, which is different from the one proved by B.Ricceri in [15] (Arch. Math. 75 (2000), 220-226) and gives an estimate of where Λ can be located. On the other hand, as an application of the previous result, we prove an existence theorem of three classical solutions for a two-point boundary value problem which is independent from the one by J.Henderson and H.B.Thompson ([10], J. Differential Equations 166 (2000), 443-454). Specifically, an example is given where the key assumption of [10] fails. Nevertheless, the existence of three solutions can still be deduced using our theorem. 1