## Existence of solutions for a semirelativistic Hartree equation with unbounded potentials.(English)Zbl 1391.35139

The paper deals with the existence of a solution to the semirelativistic Hartree equation $\sqrt{-\Delta+m^2 u }+ V(x) u = A(x)( W * | u|^p) | u|^{p-2} u$ under suitable growth assumption on the potential functions $$V$$ and $$A$$, which can be unbounded from above. The author introduces a class of function spaces and gives a compact embedding result which is the main ingredient to prove the existence result.

### MSC:

 35J60 Nonlinear elliptic equations 35Q55 NLS equations (nonlinear Schrödinger equations)

### Keywords:

Hartree equation; infinitely many solutions
Full Text:

### References:

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