Using the bounded mountain pass lemma and the Ekeland variational principle, we prove a bounded version of the Pucci-Serrin three critical points result in the intersection of a ball with a wedge in a Banach space. The localization constraints are overcome by boundary and invariance conditions. The result is applied to obtain multiple positive solutions for some semilinear problems.
Radu Precup. Patrizia Pucci. Csaba Varga. "A three critical points result in a bounded domain of a Banach space and applications." Differential Integral Equations 30 (7/8) 555 - 568, July/August 2017. https://doi.org/10.57262/die/1493863394