We consider the following Schr ̈odinger-Bopp-Podolsky system in R3 −ε2∆u+V(x)u+φu=f(u) −ε2∆φ + ε4∆2φ = 4πu2, where ε > 0 with V : R3 → R, f : R → R satisfy suitable assumptions. By using variational methods, we prove that the number of positive solutions is estimated below by the Ljusternick-Schnirelmann category of M , the set of minima of the potential V .
Positive Solutions For a Schr\"odinger-Bopp-Podolsky system in $\mathbb R^{3}$
Siciliano, Gaetano
2020-01-01
Abstract
We consider the following Schr ̈odinger-Bopp-Podolsky system in R3 −ε2∆u+V(x)u+φu=f(u) −ε2∆φ + ε4∆2φ = 4πu2, where ε > 0 with V : R3 → R, f : R → R satisfy suitable assumptions. By using variational methods, we prove that the number of positive solutions is estimated below by the Ljusternick-Schnirelmann category of M , the set of minima of the potential V .File in questo prodotto:
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