Journal of Inequalities and Applications
Volume 6 (2000), Issue 3, Pages 261-285

On a minimax problem of ricceri

Giuseppe Cordaro

Dipartimento di Matematica, Università di Messina, Sant'Agata, Messina 98166, Italy

Received 18 August 1999; Revised 20 October 1999

Copyright © 2000 Giuseppe Cordaro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let E be a real separable and reflexive Banach space, XE weakly closed and unbounded, Φ and Ψ two non-constant weakly sequentially lower sernicontinuous functionals defined on X, such that Φ+λΨ is coercive for each λ0. In this setting, if supλ0infxX(Φ(x)+λ(Ψ(x)+ρ))=infxXsupλ0(Φ(x)+λ(Ψ(x)+ρ)) for every ρR, then, one has supλ0infxX(Φ(x)+λΨ(x)+h(λ))=infxXsupλ0(Φ(x)+λΨ(x)h(λ)), for every concave function h:[0,+[R.