In this paper we consider the system in ℝ 3(0.1) -ε 2 Δu + V(x)u + Φ(x)u = u p, -ΔΦ = u 2, for p ε (1, 5). We prove the existence of multi-bump solutions whose bumps concentrate around a local minimum of the potential V(x). We point out that such solutions do not exist in the framework of the usual Nonlinear Schrödinger Equation.

Cluster solutions for the schrödinger-poisson-slater problem around a local minimum of the potential

VAIRA, Giusi
2011

Abstract

In this paper we consider the system in ℝ 3(0.1) -ε 2 Δu + V(x)u + Φ(x)u = u p, -ΔΦ = u 2, for p ε (1, 5). We prove the existence of multi-bump solutions whose bumps concentrate around a local minimum of the potential V(x). We point out that such solutions do not exist in the framework of the usual Nonlinear Schrödinger Equation.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11591/368457
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