Radial solutions for Neumann problems involving prescribed mean curvature operator in a ball and in an annular domain

Abstract

Using topological transversality method together with barrier strip technique and cut-off technique, we obtain new existence and uniqueness results of radial solutions to the Neumann problems involving prescribed mean curvature operator $\left(\begin{array}{c}\text{div}\left(\frac{\nabla v}{\sqrt{1+{|\nabla v|}^2}}\right)=f\left(\left|x\right|,v,\frac{dv}{dr}\right)in\Omega ,\\ \frac{\partial v}{\partial n}=0on\partial \Omega ,\end{array}\right)$where $\Omega =\{x\in R^N:R_1<\left|x\right|<R_2\}(0\le R_1<R_2,N\ge 2)$, $f:[R_1,R_2]\times R^2\to R$ is continuous. Meanwhile, we demonstrate the importance of our results through an illustrative example.