A positive solution branch for nonlinear eigenvalue problems in RNRN

In this note, we give sufficient conditions for the existence of a positive solution branch for the problem −Δu=λa(x)f(u)in RN,u(x)→0as |x|→∞, with sign changing weight aa, where N≥3N≥3 and ff is a smooth nonlinearity with f(0)≠0f(0)≠0.