On oscillation of integro-differential equations

Nonlinear Integro - Differential Equations

On the Oscillation of Fractional Differential Equations

In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form D ax+ f1(t, x) = v(t) + f2(t, x), lim t→a+ J1−q a x(t) = b1, where D a denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville dif...

Singular perturbations of integro-differential equations

We study the singular perturbation problem (E2) 2 2u′′ 2 (t) + u ′ 2(t) = Au2(t) + (K ∗Au2)(t) + f2(t), t ≥ 0, 2 > 0, for the integrodifferential equation (E) w′(t) = Aw(t) + (K ∗Aw)(t) + f(t), t ≥ 0, in a Banach space, when 2 → 0. Under the assumption that A is the generator of a strongly continuous cosine family and under some regularity conditions on the scalar-valued kernel K we show that p...

Positive Solutions of Volterra Integro–differential Equations

We present some sufficient conditions such that Eq. (1) only has solutions with zero points in (0,∞). Moreover, we also obtain some conditions such that Eq. (1) has a positive solution on [0,+∞). The motivation of this work comes from the work of Ladas, Philos and Sficas [5]. They discussed the oscillation behavior of Eq. (1) when P (t, s) = P (t− s) and g(t) = t. They obtained a necessary and ...

On the Stability of Delay Integro-differential Equations

Some new stability results are given for a delay integro-differential equation. A basis theorem on the behavior of solutions of delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.