On regular solutions of a nonlinear equation of Choquard's type

Abstract

Synopsis We study the nonlinear equation in ℝ 3 , where Δ denotes the Laplacian operator, and R and K are real-valued functions satisfying suitable conditions. We use a variational formulation to show the existence of a non-trivial weak solution of the above equation for some real number λ. Because of our assumptions on R and K we shall look for solutions which are spherically symmetric, decrease with r = | x | and vanish at infinity.