A generalized Lyness equation is investigated as follows x(n+1) = x(n)/(a + bx(n)) x(n-1), n = 0,1,2,..., (*) where a,b is an element of [0, infinity) with a + b > 0 and where the initial values x(-1),x(0) are arbi...A generalized Lyness equation is investigated as follows x(n+1) = x(n)/(a + bx(n)) x(n-1), n = 0,1,2,..., (*) where a,b is an element of [0, infinity) with a + b > 0 and where the initial values x(-1),x(0) are arbitrary positive numbers. Same new results, mainly a necessary and sufficient condition for the periodicity of the solutions of Eq.(*) and a sufficient condition for the strict oscillation of all solutions of Eq (*), are obtained. As an application, the results solve an open problem presented by G. Ladas.展开更多
文摘A generalized Lyness equation is investigated as follows x(n+1) = x(n)/(a + bx(n)) x(n-1), n = 0,1,2,..., (*) where a,b is an element of [0, infinity) with a + b > 0 and where the initial values x(-1),x(0) are arbitrary positive numbers. Same new results, mainly a necessary and sufficient condition for the periodicity of the solutions of Eq.(*) and a sufficient condition for the strict oscillation of all solutions of Eq (*), are obtained. As an application, the results solve an open problem presented by G. Ladas.
