Abstract. In the paper we consider the following quasilinear Schro ̈dinger–Poisson system in the whole space R3 −ε2∆u+(V +φ)u=u|u|p−1 −∆φ − β∆4φ = u2, where1<5,β>0,V :R3 →]0,∞[,andlookforsolutionsu,φ:R3 →Rinthe semiclassical regime, namely when ε → 0. By means of the Lyapunov–Schmidt method we estimate the number of solutions by the cup-length of the critical manifold of the external potential V .
Existence and concentration of semiclassical bound states for a quasilinear Schrödinger-Poisson system
Gaetano Siciliano
;
2024-01-01
Abstract
Abstract. In the paper we consider the following quasilinear Schro ̈dinger–Poisson system in the whole space R3 −ε2∆u+(V +φ)u=u|u|p−1 −∆φ − β∆4φ = u2, where1<5,β>0,V :R3 →]0,∞[,andlookforsolutionsu,φ:R3 →Rinthe semiclassical regime, namely when ε → 0. By means of the Lyapunov–Schmidt method we estimate the number of solutions by the cup-length of the critical manifold of the external potential V .File in questo prodotto:
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