Positive solutions to a Kirchhoff problem with sign-changing and non-Lipschitz nonlinearities

Let Ω be a bounded smooth domain in (Formula presented.) ((Formula presented.)), (Formula presented.), where (Formula presented.), and (Formula presented.), and let (Formula presented.). We investigate the structure of the set of couples of positive parameters (Formula presented.) such that the nonlocal Kirchhoff problem (Formula presented.) admits at least a weak solution. In particular, we partially extend a previous result, obtained for the case b = 0, to the nonlocal case (Formula presented.). Some open questions are also pointed out.