We consider the following fractional Schrodinger-Poisson type equation with magnetic fieldsepsilon(2s) (-Delta)(s)(A/epsilon) u + V(x)u + epsilon(-2t) (vertical bar x vertical bar(2t-3) * vertical bar u vertical bar(2))u = f (vertical bar u vertical bar(2))u in R-3,where epsilon > 0 is a parameter, s is an element of (3/4, 1), t is an element of (0, 1), (-Delta)(s)(A) is the fractional magnetic Laplacian, A : R-3 -> R-3 is a smooth magnetic potential, V : R-3 -> R is a positive continuous electric potential and f : R -> R is a continuous function with subcritical growth. Using suitable variational methods, we show the existence of a family of nontrivial solutions which concentrates around global minima of the potential V(x) as epsilon -> 0.

Existence and concentration of nontrivial solutions for a fractional magnetic Schrodinger-Poisson type equation / Ambrosio, V. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - 21:(2020), pp. 1023-1061.

### Existence and concentration of nontrivial solutions for a fractional magnetic Schrodinger-Poisson type equation

#### Abstract

We consider the following fractional Schrodinger-Poisson type equation with magnetic fieldsepsilon(2s) (-Delta)(s)(A/epsilon) u + V(x)u + epsilon(-2t) (vertical bar x vertical bar(2t-3) * vertical bar u vertical bar(2))u = f (vertical bar u vertical bar(2))u in R-3,where epsilon > 0 is a parameter, s is an element of (3/4, 1), t is an element of (0, 1), (-Delta)(s)(A) is the fractional magnetic Laplacian, A : R-3 -> R-3 is a smooth magnetic potential, V : R-3 -> R is a positive continuous electric potential and f : R -> R is a continuous function with subcritical growth. Using suitable variational methods, we show the existence of a family of nontrivial solutions which concentrates around global minima of the potential V(x) as epsilon -> 0.
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2020
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11566/296926`
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