Existence and Uniqueness of Positive Solitons for a Second-Order Difference Equation - Xinfu Li; Guang Zhang; Ying Wang (Discrete Dynamics in Nature and Society)
A discrete logistic steady-state equation with both positive and negative birth rate of population will be considered. By using sub- and upper-solution method, the existence of bounded positive solutions and the existence and uniqueness of positive solitons will be established. To this end, the Dirichlet eigenvalue problem with positive and negative coefficients is considered, and a general sub- and upper-solution theorem is also obtained.