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

DOI: http://dx.doi.org/10.12775/TMNA.2001.005

#### 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

${\mathbb R}^N$.

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

${\mathbb R}^N$.

#### Keywords

Critical point theory; elliptic problem on R^N

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