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This paper focuses on the existence and the multiplicity of classical radially symmetric solutions of the mean curvature problem:−div∇v1+|∇v|2=f(x,v,∇v)inΩ,a0v+a1∂v∂ν=0on∂Ω,\left\{\begin{array}{ll}-\text{div}\left(\frac{\nabla v}{\sqrt{1+|\nabla v{|}^{2}}}\right)=f(x,v,\nabla v)&amp; \text{in}\hspace{.5em}\text{&amp;#x03A9;},\\ {a}_{0}v+{a}_{1}\tfrac{\partial v}{\partial \nu }=0&amp; \text{on}\hspace{.5em}\partial \text{&amp;#x03A9;},\end{array}\right.withΩ\text{&amp;#x03A9;}an open ball inℝN{{\mathbb{R}}}^{N}, in the presence of one or more couples of sub- and super-solutions, satisfying or not satisfying the standard ordering condition. The novel assumptions introduced on the function  f  allow us to complement or improve several results in the literature.

Revisiting the sub- and super-solution method for the classical radial solutions of the mean curvature equation