Forced oscillation of impulsive fractional partial differential equations

In this paper, we investigate the forced oscillation of impulsive fractional partial differential equations. Some sufficient conditions are established which guarantee that the oscillation of the solutions by applying the integral transformation technique and differential inequality method. Also an example is shown to illustrate the effectiveness of our main results

Convergence of the positive solutions of a nonlinear neutral difference equation

Sufficient conditions are established which guarantee the convergence of the positive solutions of the neutral type difference equation of the form ∆[x(n) − q(n)x(σ(n))] + p(n)f(x(τ1(n)), . . . , x(τk(n))) = 0, where σ(n), n = 1, 2, . . . , are retarded arguments and τj (n), j = 1, . . . , k, are general deviated arguments.Знайдено достатнi умови збiжностi додатних розв’язкiв рiзницевого рiвняння нейтрального типу вигляду ∆[x(n) − q(n)x(σ(n))] + p(n)f(x(τ1(n)), . . . , x(τk(n))) = 0, де σ(n), n = 1, 2, . . . , — запiзнiлi аргументи i τj (n), j = 1, . . . , k, — загальнi вiдхиленi аргументи