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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)
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