Abstract: By using the Leray-Schauder fixed point theorem, we discuss the existence of radial symmetric solutions for the boundary value problem of the p-Laplace equation with nonlinear gradient term, where  p>1, f: ［r₁,r₂］×R×R⁺→R is continuous. When 1λ_p,1 of the p-Laplace operator -Δ_pu under the boundary condition, an existence result of radial symmetric solutions is obtained.

Key words: p-Laplace equation, annular domain, radial symmetric solution, nonlinear gradient term, Leray-Schauder fixed point theorem