Composition theorems of Stepanov almost periodic functions and Stepanov-like pseudo-almost periodic functions.
Conditions of existence quasiperiodic solutions for some nonlinear differential equations of second order and third power
Conditions of existence quasiperiodic solutions for some ordinary differential equations of first and second order
Convexity, boundedness, and almost periodicity for differential equations in Hilbert space.
Dynamics of logistic equations with non-autonomous bounded coefficients.
Ergodicity and asymptotically almost periodic solutions of some differential equations.
Existence of almost automorphic solutions to some classes of nonautonomous higher-order differential equations.
Existence of almost periodic solutions of systems of linear and quasilinear differential equations with time lag
Existence of almost-periodic ultra-weak solutions to the equation in Hilbert spaces
Existence of square-mean almost periodic mild solutions to some nonautonomous stochastic second-order differential equations.
Existence theorems for almost periodic solutions of first-order differential equations
Exponential decay and existence of almost periodic solutions for some linear forced differential equations.
Further properties of Stepanov--Orlicz almost periodic functions
We revisit the concept of Stepanov--Orlicz almost periodic functions introduced by Hillmann in terms of Bochner transform. Some structural properties of these functions are investigated. A particular attention is paid to the Nemytskii operator between spaces of Stepanov--Orlicz almost periodic functions. Finally, we establish an existence and uniqueness result of Bohr almost periodic mild solution to a class of semilinear evolution equations with Stepanov--Orlicz almost periodic forcing term.
Global exponential stability of pseudo almost automorphic solutions for delayed Cohen-Grosberg neural networks with measure
We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a -pseudo almost automorphic solution. The...
Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity [Book]
Invariant tori for periodically perturbed oscillators.
The response of an oscillator to a small amplitude periodic excitation is discussed. In particular, sufficient conditions are formulated for the perturbed oscillator to have an invariant torus in the phase cylinder. When such an invariant torus exists, some perturbed solutions are in the basin of attraction of this torus and are thus entrained to the dynamical behavior of the perturbed system on the torus. In particular, the perturbed solutions in the basin of attraction of the invariant torus are...
Lagrangian stability of a class of second-order periodic systems.
Linear differential equations with quasiperiodic coefficients
Liouville type results for periodic and almost periodic linear operators
New criteria for the existence of periodic and almost periodic solutions for some evolution equations in Banach spaces.