Infinitely many regular weak solutions for odd symmetric prescribed mean curvature problems

We establish in this paper the existence of infinitely many regular weak solutions of the prescribed mean curvature problem \begin{equation*} -{\rm div } \Big({\nabla u}/{ \sqrt{1+{|\nabla u|}^2}}\Big) = f(x,u) \mbox{\, in $\Omega$}, \qquad \mathcal{B} u=0 \mbox{\, on $\partial \Omega$}. \end{equation*} where $\Omega$ is a bounded domain in $ \RR^N$ with a $C^1$ boundary $\partial \Omega$, $\BB$ is either the Dirichlet, or the Neumann, or the mixed boundary operator, the function $f(x,s)$ is odd with respect to $s\in \RR$ and has a potential $F(x,s)=\int_0^s f(x,t)\,dt$ which is desultorily subquadratic at $s=0$, locally with respect to $x\in \Omega$. Our findings improve and extend in various directions previous results established in the literature.