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.File in questo prodotto:
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