Symmetry and monotonicity results for solutions of semilinear PDEs in sector-like domains

Abstract In this paper we consider semilinear PDEs, with a convex nonlinearity, in sector-like domain. Using cylindrical coordinates $$(r, \theta , z)$$ ( r , θ z ) investigate the shape of possibly sign-changing solutions whose derivative $$\theta$$ vanishes at boundary. We prove that any solution Morse index less than two must be either independent or strictly monotone respect to . special case planar domain, result holds circular sector as well an annular one, and it can also extended rectangular The corresponding problem higher dimensions is considered, extension unbounded domains. proof based on rotating-plane argument: convenient manifold introduced order avoid overlapping domain its reflected image where opening larger $$\pi$$ π