Existence of monotone positive solution of neutral partial difference equation
The paper deals with the neutral partial difference equation \[ \sum^u_{i=1} [T(\Delta_1, \Delta_2)(\theta(\lambda) y_{m,n}+ cy_{m- k_i, n-\ell_i})+ p_i(m,n) y_{m-\sigma_i, n-\tau_i}]= 0, \] where \(T(\Delta_1,\Delta_2)= \Delta_1+ \Delta_2+ I\), \(\Delta_1 y_{m,n}= y_{m+1,n}- y_{m,n}\), and \(\Delta_2 y_{m,n}= y_{m,n+1}- y_{m,n}\), \(Iy_{m,n}= y_{m,n}\). The authors prove existence of monotone eventually positive solutions.
existence of monotone positive solutions
scientific article; zbMATH DE number 1497251