A supercritical scalar field equation with a forcing term

Abstract

This paper is concerned with the elliptic problem for a scalar field equation with a forcing term −Δu+u=up+κμ in RN, where N≥2, p>1, κ>0 and μ is a Radon measure in RN with a compact support. Under a suitable integrability condition on μ, we give a complete classification of the existence and nonexistence of positive solutions decaying at the space infinity in the case of 1<p<pJL. Here pJL is the so-called Joseph-Lundgren exponent.