In this paper we consider the following critical Schrödinger–Bopp–Podolsky system in the unknowns u,φ : R3 → R and where ε,a > 0 are parameters. The functions V, K, Q satisfy suitable assumptions as well as the nonlinearity h which is subcritical. For any fixed a > 0, we show existence of “small” solutions in the semiclassical limit, namely whenever ε → 0. We give also estimates of the norm of this solutions in terms of ε. Moreover, we show also that fixed ε suitably small, when a → 0 the solutions found strongly converge to solutions of the Schrödinger-Poisson system.
Critical Schrödinger–Bopp–Podolsky systems: solutions in the semiclassical limit
Gaetano Siciliano
2024-01-01
Abstract
In this paper we consider the following critical Schrödinger–Bopp–Podolsky system in the unknowns u,φ : R3 → R and where ε,a > 0 are parameters. The functions V, K, Q satisfy suitable assumptions as well as the nonlinearity h which is subcritical. For any fixed a > 0, we show existence of “small” solutions in the semiclassical limit, namely whenever ε → 0. We give also estimates of the norm of this solutions in terms of ε. Moreover, we show also that fixed ε suitably small, when a → 0 the solutions found strongly converge to solutions of the Schrödinger-Poisson system.File in questo prodotto:
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