Multiplicity of global minima for parametrized functions
Biagio Ricceri · Rendiconti Lincei Matematica e Applicazioni · 2010
Let X be a topological space, I a real interval and \Psi a real-valued function on X\times I . In this paper, we prove that if \Psi is lower semicontinuous and inf-compact in X , quasiconcave and continuous in I and satisfies \sup_I \inf_X \Psi < \inf_X \sup_I \Psi , then there exists λ^*\in I such that \Psi (\cdot ,λ^*) has at least two global minima. An application involving the integral functional of the calculus of variations is also presented.