## 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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### References:

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