This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. Using impulsive periodic evolution operator given by us, the T0-periodic PC-mild solution is introduced and suitable Poincaré operator is constructed. Showing the compactness of Poincaré operator and using a new generalized Gronwall’s inequality with impulse, mixed type integral operators and B-norm...

We derive explicit stability conditions for time-dependent difference equations with several delays in C n (the set of n complex vectors) and estimates for the size of the solutions. The growth rates obtained here are not necessarily decay rates. 1. Introduction. Stability of systems of difference equations with delays has been discussed by many authors, for example, see Gil' and Cheng [6], Zha...

We present a criterion for absence of eigenvalues for one-dimensional Schrödinger operators. This criterion can be regarded as an L1-version of Gordon’s theorem and it has a broader range of application. Absence of eigenvalues is then established for quasiperiodic potentials generated by Liouville frequencies and various types of functions such as step functions, Hölder continuous functions and...

In this paper, some new discrete Gronwall-Bellman-Ou-Iang-type inequalities are established. These on the one hand generalize some existing results and on the other hand provide a handy tool for the study of qualitative as well as quantitative properties of solutions of difference equations.

We present a uniform L-stability estimate for mild solutions to the Fokker-Planck-Boltzmann equation. For stability estimate, we derive a Gronwall type estimate using dispersion estimates for mild solutions due to the hypoelliptic structure of the Vlasov-Fokker-Planck operator.

Asymptotic equilibria of linear integro-differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro-differential equations are established. A new Gronwall–Bellman type lemma for integro-differential inequalities is proved. An example is given to demonstrate the validity of one of the results. c © 2008 Elsev...