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

Let ₙ≥0 be the sequence of Jacobsthal- Lucas number, that is given by the relation j₀=2, j₁=1, jₙ=jₙ₋₁+2jₙ₋₂ for all n≥2. In this paper, we study the solutions $(X,Y,Z)$ of the following equation that is so called the Jin-Schmidt equation: {equation*} AX^2 + BY^2 +CZ^2 = DXYZ+1, {equation*} where X=jᵢ, Y=jⱼ and Z=jₖ with i,j,k≥ 1.