Li, L. Zhao and L. Maqbul , Almost periodic solutions of neutral functional differential equations with Stepanov-almost periodic terms, Electron. Bahuguna , Almost periodic solutions for Stepanov-almost periodic differential equations, Differ.

Stepanov , Uber einige Verallgemeinerungen der fastperiodischen Funktionen, Mathematische Annalen , 95 , Feng , A non-autonomous Hamiltonian system on time scales, Nonlinear Anal. Feng , Homoclinic orbits and periodic solutions for a class of Hamiltonian systems on time scales, J. Wang and Y. Li, Weighted pseudo almost automorphic functions with applications to abstract dynamic equations on time scales, Ann. Yang and Y. Li, Existence and global exponential stability of almost periodic solutions for a class of delay duffing equations on time scales, Abstr. Jiang , Almost periodic solutions for neutral type BAM neural networks with distributed leakage delays on time scales, Neurocomputing , , On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations.

Junhao Hu , Chenggui Yuan. Strong convergence of neutral stochastic functional differential equations with two time-scales. Existence of periodic solutions of dynamic equations on time scales by averaging. Mostafa Fazly , Mahmoud Hesaaraki. Periodic solutions for a semi-ratio-dependent predator-prey dynamical system with a class of functional responses on time scales.

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Sung Kyu Choi , Namjip Koo. Stability of linear dynamic equations on time scales. Conference Publications , , Special : Kaymakcalan , R. Mert , A. Asymptotic equivalence of dynamic systems on time scales. Firing map of an almost periodic input function. Periodic and almost periodic oscillations in a delay differential equation system with time-varying coefficients. Raegan Higgins.

Asymptotic behavior of second-order nonlinear dynamic equations on time scales.

Chunhong Li , Jiaowan Luo. Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients. Denis Pennequin. Existence of almost periodic solutions of discrete time equations. Value function for regional control problems via dynamic programming and Pontryagin maximum principle. Yunfei Peng , X.

A class of nonlinear impulsive differential equation and optimal controls on time scales. Saroj Panigrahi. Liapunov-type integral inequalities for higher order dynamic equations on time scales. Conference Publications , , special : We remark that the connection between Eq. We also need the following two theorems. The first one is a well-known consequence of the half-linear Roundabout theorem which is proved, e.

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For the second one, we can refer to [4, Theorem 2. Theorem 3. The Riccati equation associated to Eq. In fact, we will use only partial cases of Theorems 3.

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## Almost Periodic Differential Equations

For reader's convenience, we mention the corresponding corollaries for Eq. Corollary 3. There exists a negative solution Z of the adaptedRiccati equation 3. Proof We apply Theorem 3. Inequality 3.

Thus, 3. Let us consider an arbitrary solution w of Eq. We know that w is decreasing which follows immediately from 3. By combination of 3. This observation implies the existence of a negative solution Z of Eq. Theorem 4. By contradiction, we suppose that Eq.

We recall see 3. In addition, considering 4. Using the fact that this function has the Lipschitz property and using 4. In the second part of the proof, we have to show that Eq. Analogously see 4. Thus, we can define. On the contrary, we will assume that such a number S does not exist. We estimate the value -' t1 by the following expression:. We consider T, a as sufficiently large numbers for which 4. Analogously, we can require that T and a are so large that. Thus, for sufficiently large T, we can assume that. Similarly as in the first part of the proof see 4. From Corollary 3. Remark 2 Our result is 'backward compatible' with previous results about the conditional oscillation of half-linear equations.

More precisely, if the functions r and s in Eq. It holds. The statement of Theorem 4. Then the oscillation constant is.

- Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations.
- Periodic function.
- Almost Periodic Functions: Second Edition.
- Power Transmissions: Proceedings of the International Conference on Power Transmissions 2016;

If the functions r and s in Eq. Note that the main result of [17] cannot be used for general periodic functions r, s which do not have any common period. This situation is illustrated by the following example.

## Weighted pseudo almost periodic functions and applications - EM|consulte

It is also seen that 4. Such functions can be constructed using, e. Based on this fact, we conjecture that there exist almost periodic functions ri, si, r2, s2 satisfying 4.