A multiplicity result for a semilinear Maxwell type equation

Antonio Azzollini

DOI: http://dx.doi.org/10.12775/TMNA.2008.005

Abstract


In this paper we look for solutions of the equation
$$
\delta d\text{\bf A}=f'(\langle\text{\bf A},\text{\bf A}\rangle)\text{\bf A}\quad \text{in }\mathbb R^{2k},
$$
where $\text{\bf A}$ is a $1$-differential form and $k\geq 2$. These solutions
are critical points of a functional which is strongly indefinite
because of the presence of the differential operator $\delta d$.
We prove that, assuming a suitable convexity condition on the
nonlinearity, the equation possesses infinitely many finite energy
solutions.

Keywords


Semilinear Maxwell equations; strongly indefinite functional; Strong convexity

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