Nonexistence Results for the Schrödinger-Poisson Equations with Spherical and Cylindrical Potentials in ℝ3

الملخص EN

We study the following Schrödinger-Poisson system: -Δu+V(x)u+ϕu=|u|p-1u, -Δϕ=u2, lim|x|→+∞ϕ(x)=0, where u,ϕ:ℝ3→ℝ are positive radial functions, p∈(1,+∞), x=(x1,x2,x3)∈ℝ3, and V(x) is allowed to take two different forms including V(x)=1/(x12+x22+x32)α/2 and V(x)=1/(x12+x22)α/2 with α>0.

Two theorems for nonexistence of nontrivial solutions are established, giving two regions on the α-p plane where the system has no nontrivial solutions.