A multiplicity result for a semilinear Maxwell type equation
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Semilinear Maxwell equations, strongly indefinite functional, Strong convexityAbstrakt
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.Pobrania
Opublikowane
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 marzec 2008, T. 31, nr 1, s. 83–110. [udostępniono 22.7.2024].
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