Minimax results for semicoercive functionals with application to differential equations (Q949841)

The author proves that if \(f:X\times Y\to \mathbb R\) is lower semicontinuous, semicoercive and nearly subconvexlike on \(Y\) (in a certain sense) and nearly subconcavlike on \(X\), then \(\min_Y\, \sup_Xf=\sup_X\, \min_Y f\). Here, \(X\neq \emptyset\) and \(Y\) is a linear topological space, in which compactness, countable compactness and sequential compactness are equivalent. A theorem on the existence of saddle points, as well as an application to differential equations are presented, too.