Multiplicity of global minima for parametrized functions

作者：Ricceri Biagio^*

来源：Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 2010, 21(1): 47-57.

DOI：10.4171/RLM/560

• Multiplicity
• global minimum
• parametric optimization
• minimax inequality

Let X be a topological space, I a real interval and Psi a real-valued function on X x I. In this paper, we prove that if C is lower semicontinuous and inf-compact in X, quasi-concave and continuous in I and satisfies sup(I) inf(X) Psi < inf(X) sup(I) Psi, then there exists lambda* is an element of I such that Psi(.,lambda*) has at least two global minima. An application involving the integral functional of the calculus of variations is also presented.

• 出版日期2010