A Note on Symmetry of Solutions for a Class of Singular Semilinear Elliptic Problems

Abstract

Abstract We prove symmetry and monotonicity properties for positive solutions of the singular semilinear elliptic equation - Δ ⁢ u = g ⁢ ( x ) u γ + h ⁢ ( x ) ⁢ f ⁢ ( u ) $-\Delta u=\frac{g(x)}{u^{\gamma}}+h(x)f(u)$ in bounded smooth domains with zero Dirichlet boundary conditions. The well-known moving plane method is applied.