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Infinitely many solutions for Schrödinger-Maxwell equations with indefinite sign subquadratic potentials. (English) Zbl 1358.35027

Summary: In this paper, we deal with multiplicity of solutions of a class of sublinear Schrödinger-Maxwell equations \[ \begin{cases}-\Delta u+V(x)u+\phi u=f(x,u) \quad &\text{ in }\mathbb R^3,\\ -\Delta\phi =u^2, \quad \lim\limits_{| x| \to \infty} \phi (x)=0 &\text{ in }\mathbb R^3.\end{cases} \] Under more relaxed assumptions on \( V\) and \( f\), we establish some existence criteria to guarantee that the above problem has at least one or infinitely many nontrivial solutions by using the genus properties in critical theory.

MSC:

35J47 Second-order elliptic systems
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