A multiplicity result for a semilinear Maxwell type equation - Azzollini, Antonio (Topological Methods in Nonlinear Analysis, 2008)
In this paper we look for solutions of the equation $$ δ d\text{\bf A}=f'(\langle\text{\bf A},\text{\bf A}\rangle)\text{\bf A}\quad \text{in }\mathbb R^{2k}, $$where $\text{\bf A}$ is a $1$-differential form and $k≥ 2$. These solutionsare critical points of a functional which is strongly indefinitebecause of the presence of the differential operator $δ d$.We prove that, assuming a suitable convexity condition on thenonlinearity, the equation possesses infinitely many finite energysolutions.