The authors establish a result on existence of multiple solutions for a particular class of second order Sturm-Liouville boundary value problems. To be more precise, let , let with and consider the boundary value problem
where , is an -Carathérodory function, and is a positive real parameter. Then the main result of the paper (Theorem 3.1) provides sufficient conditions on in order to ensure the existence of an open interval for which the above problem has at least three weak solutions whenever
It is worth pointing out that Theorem 3.1 improves a result of Y. Tian and W. Ge [Rocky Mountain J. Math. 38, 309–327 (2008; Zbl 1171.34019)] in the sense that its assumptions are much simpler than those of the above mentioned paper.
The proof of Theorem 3.1 is based on the fact that an adequate (coercive) functional , defined on the Sobolev space equipped with the norm
has at least three critical points for each