Symmetry and monotonicity property of a solution of (p, q) Laplacian equation with singular terms

This paper examines the behavior of a positive solution u is an element of C-1,C-alpha(B-R(x(0)))($$$) over bar of the (p, q) Laplace equation with a singular term and zero Dirichlet boundary condition. Specifically, we consider the equation {-div(|del u|(p-2)del u + a(x)|del u|(q-2)del u) = g(x)/u(delta) + h(x) f(u) in B-R(x(0)), {u = 0 on partial derivative B-R(x(0)). We assume that 0 < delta < 1, 1 < p <= q < infinity, and f is a C-1(R) nondecreasing function. Our analysis uses the moving plane method to investigate the symmetry and monotonicity properties of u. Additionally, we establish a strong comparison principle for solutions of the (p, q) Laplace equation with radial symmetry under the assumptions that 1 < p <= q <= 2 and f = 1.