A three critical points theorem and its applications to the ordinary Dirichlet problem (Q1876354)

In the first part of the present paper the authors establish an abstract result related to the existence of at least three critical points for energy functionals depending on a real parameter \(\lambda\in\Lambda\). They also prove an estimate on the location of the set \(\Lambda\). The main result of this paper generalizes in a nontrivial way the well-known Ricceri's critical point theorem established in [\textit{B. Ricceri}, Arch. Math. 75, No. 3, 220--226 (2000; Zbl 0979.35040)]. In the second part this abstract result is applied to establish a multiplicity result for a class of nonlinear Sturm-Liouville problems. The proofs are based on specific tools of the variational calculus combined with adequate elliptic estimates. Reviewer's remark: The abstract result established in the paper can be applied in the treatment of wide classes of two-point boundary value problems.