We study the semiclassical limit for the following system of Maxwell-Schrodinger equations: -(h^2/2m)∆v+v+ωφv−γv^p=0, −∆φ=4πωv^2, where h, m, ω, γ > 0, v, φ : R3 → R, 1 < p < 11/7. This system describes standing waves for the nonlinear Schrodinger equation interacting with the electrostatic field: the unknowns v and φ represent the wave function associated to the particle and the electric potential respectively. By using localized energy method, we construct a family of positive radially symmetric bound states (v_h,φ_h) such that v_h concentrates around a sphere {|x|=s_0} when h→0.
D'Aprile, T.c., Wei, J. (2005). On bound states concentrating on spheres for the Maxwell-Schrödinger equation. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 37(1), 321-342 [10.1137/S0036141004442793].
On bound states concentrating on spheres for the Maxwell-Schrödinger equation
D'APRILE, TERESA CARMEN;
2005-01-01
Abstract
We study the semiclassical limit for the following system of Maxwell-Schrodinger equations: -(h^2/2m)∆v+v+ωφv−γv^p=0, −∆φ=4πωv^2, where h, m, ω, γ > 0, v, φ : R3 → R, 1 < p < 11/7. This system describes standing waves for the nonlinear Schrodinger equation interacting with the electrostatic field: the unknowns v and φ represent the wave function associated to the particle and the electric potential respectively. By using localized energy method, we construct a family of positive radially symmetric bound states (v_h,φ_h) such that v_h concentrates around a sphere {|x|=s_0} when h→0.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
