Solutions of a Markoff type equation in the Jacobsthal- Lucas numbers

Let $\{j_n\}_{n\geq0}$ be the sequence of Jacobsthal- Lucas number, that is given by the relation $j_0=2$, $j_1=1$, $j_n=j_{n-1}+2j_{n-2}$ for all $n\geq2$. In this paper, we study the solutions $(X,Y,Z)$ of the following equation that is so called the Jin-Schmidt equation: \begin{equation*} AX^2 + BY^2 +CZ^2 = DXYZ+1, \end{equation*} where $X=j_i$, $Y=j_j$ and $Z=j_k$ with $i,j,k\geq 1$.