Let X be a topological space, I a real interval and ψ a real-valued function on X x I. In this paper, we prove that if ψ is lower semicontinuous and inf-compact in X, quasiconcave and continuous in I and satisfies sup_I_ inf_X_ ψ < inf_X_ sup_I_ ψ, then there exists λ*∈ I such that ψ (∙,λ*) has at least two global minima. An application involving the integral functional of the calculus of variations is also presented.
Cite this article
Biagio Ricceri, Multiplicity of global minima for parametrized functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 1, pp. 47–57DOI 10.4171/RLM/560