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Potential well and multiplicity of solutions for nonlinear Dirac equations

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  • In this paper we consider the semi-classical solutions of a massive Dirac equations in presence of a critical growth nonlinearity

    $ -i\hbar \sum\limits_{k = 1}^{3}\alpha_k\partial_k w+a\beta w+V(x)w = f(|w|)w. $

    Under a local condition imposed on the potential $ V $, we relate the number of solutions with the topology of the set where the potential attains its minimum. In the proofs we apply variational methods, penalization techniques and Ljusternik-Schnirelmann theory.

    Mathematics Subject Classification: 35Q40, 49J35.


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