A multiplicity result for a semilinear Maxwell type equation
Keywords
Semilinear Maxwell equations, strongly indefinite functional, Strong convexityAbstract
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.Downloads
Published
2008-03-01
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1.
AZZOLLINI, Antonio. A multiplicity result for a semilinear Maxwell type equation. Topological Methods in Nonlinear Analysis. Online. 1 March 2008. Vol. 31, no. 1, pp. 83 - 110. [Accessed 28 March 2024].
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