Abstract
In this paper, we are concerned with the multiplicity of nontrivial solutions for the following class of complex problems
where \({\Omega \subset \mathbb{R}^N(N \geq 4)}\) is a bounded domain with smooth boundary, \({A: \overline{\Omega} \rightarrow \mathbb{R}^N}\) is a continuous magnetic potential and \({2 \leq q < 2^* = \frac{2N}{N-2}}\). Using the Lusternik-Schnirelman theory, we relate the number of solutions with the topology of Ω.
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The authors were supported by INCT-MAT, PROCAD, CNPq/Brazil 301807/2013-2, 03080/2009- 4, and 301242/2011-9.
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Alves, C.O., Figueiredo, G.M. Multiple Solutions for a Semilinear Elliptic Equation with Critical Growth and Magnetic Field. Milan J. Math. 82, 389–405 (2014). https://doi.org/10.1007/s00032-014-0225-7
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DOI: https://doi.org/10.1007/s00032-014-0225-7