On a generalized critical point theory on gauge spaces and applications to elliptic problems on ${\mathbb R}^N$

Abstract

In this paper, we introduce some aspects of a critical point theory for multivalued functions $\Phi : E \to {\mathbb R}^{\mathbb N} \cup \{\infty\}$ defined on $E$ a complete gauge space and with closed graph. The existence of a critical point is established in presence of linking. Finally, we present applications of this theory to semilinear elliptic problems on ${\mathbb R}^N$.