Asymptotic Behavior of Certain Integrodifferential Equations

This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: (a(t)x\u27(t))\u27 = e (t) + ∫ tc (t - s)α - 1k(t,s)ƒ(s,x(s))ds, c \u3e 1, 0 \u3c α \u3c 1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations

Periodic solutions for a Cauchy problem on time scales

AbstractThis paper firstly shows that there does not exist a nonzero periodic solution for a nonhomogeneous Cauchy problem by using the Laplace transformation on time scales. Secondly, two new Gronwall inequalities, which play an important role in the qualitative analysis of differential and integral equations, are established. Thirdly, by employing the contraction mapping principle, existence and uniqueness results of weighted S-asymptotically ω-periodic solutions for nonlinear Cauchy problem on time scales are obtained in an asymptotically periodic function space. Finally, some examples are presented to illustrate some of the results described here

Oscillatory behavior of integro-dynamic and integral equations on time scales

By making use of asymptotic properties of nonoscillatory solutions, the oscillation behavior of solutions for the integro-dynamic equatio