AMBROSETTI-PRODI TYPE RESULTS FOR DISCRETE MINKOWSKI-MEAN CURVATURE OPERATORS WITH REPULSIVE SINGULARITIES

In this work, we study an Ambrosetti-prodi type results for discrete Minkowski-mean curvature operators with repulsive singularities <p class="disp_formula">$ \begin{align*} &amp;\triangle\Big(\frac{\triangle u(t-1)}{\sqrt{1-(\triangle u(t-1))^{2}}}\Big)+f(u)\triangle u(t)+g(t,u (t))=s,\quad t\in[1,T]_{\mathbb{Z}},\nonumber\\ &amp;u(0)=u(T),\quad \triangle u(0)=\triangle u(T), \end{align*} $ where $ f:(0,+\infty)\rightarrow \mathbb{R} $ is a continuous $ T $-periodic function, $ g:[1,T]_{\mathbb{Z}}\times(0,+\infty)\rightarrow \mathbb{R} $ is a continuous $ T $-periodic function with a repulsive singularity at the origin, and $ s\in \mathbb{R} $ is a parameter, $ T\geq2 $ is integer.