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Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system

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  • In this paper, we study the following system

    $-\epsilon^2\Delta v+V(x)v+\psi(x)v=v^p, \quad x\in R^3,$

    $-\Delta\psi=\frac{1}{\epsilon}v^2,\quad \lim_{|x|\rightarrow\infty}\psi(x)=0,\quad x\in R^3,$

    where $\epsilon>0$, $p\in (3,5)$, $V$ is positive potential. We relate the number of solutions with topology of the set where $V$ attain their minimum value. By applying Ljusternik-Schnirelmann theory, we prove the multiplicity of solutions.

    Mathematics Subject Classification: Primary: 35Q55; Secondary: 35J10, 35B35.

    Citation:

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