Results 241 to 250 of about 569,475 (279)

Almost periodic homogeneous linear difference systems without almost periodic solutions

Journal of Difference Equations and Applications, 2012
Almost periodic homogeneous linear difference systems are considered. It is supposed that the coefficient matrices belong to a group. The aim was to find such groups that the systems having no non-trivial almost periodic solution form a dense subset of the set of all considered systems.
openaire   +1 more source

Discontinuous Almost Periodic Solutions

2019
The research of discontinuous almost periodic solutions is much more complicated than that for the continuous counterpart. It requests significant development of not only properties for the functions themselves, but also new conditions for the impulsive systems, which suppose to admit the solutions.
openaire   +1 more source

Nonresonance Conditions for the Existence of Almost Periodic Solutions of Almost Periodic Systems

SIAM Journal on Applied Mathematics, 1971
For complex systems of the form \[ x' = Ax + \varepsilon g( {t,x,\varepsilon } ) , \] where A is a square matrix, g is analytic in the components of x and almost periodic in t, and $\varepsilon $ is a complex parameter, we give conditions on the Fourier exponents of g and the eigenvalues of A such that for $\| \varepsilon |$ sufficiently small, the ...
Fink, A. M., Seifert, G.
openaire   +1 more source

Almost periodic solutions for nonlinear duffing equations

Acta Mathematica Sinica, 1997
Consider the Duffing differential equation \[ d^2x/dt^2- x+ x^3= f(t),\tag{\(*\)} \] where \(f\) is almost periodic. By using the theory of exponential dichotomy, the author first proves that \((*)\) has a unique bounded solution provided \(|f|\leq 8/27\).
openaire   +2 more sources

Asymptotically Almost Periodic Solutions of Differential Equations

SIAM Journal on Applied Mathematics, 1969
In this paper we examine asymptotically almost periodic solutions of an almost autonomous differential equation. Solutions of this type have been examined previously for plane systems by Wong and Burton [8] and Utz and Waltman [6]. In both of the above papers solutions of the almost autonomous equation spiral to a periodic orbit of the limiting ...
openaire   +1 more source

Almost Periodic Solutions of the KdV Equation

SIAM Review, 1976
In this talk we discuss the almost periodic behavior in time of space periodic solutions of the KdV equation \[ u_t + uu_x + u_{xxx} = 0.\] We present a new proof, based on a recursion relation of Lenart, for the existence of an infinite sequence of conserved functionals $F_n (u)$ of form$\int {P_n (u)dx} $, $P_n $ a polynomial in u and its derivatives;
openaire   +1 more source

On Almost Periodic Solutions of Differential Equations

The Annals of Mathematics, 1959
(1.1) Z= F(z, p, t) It is assumed that for p a=0,c system (1.1) possesses a stable almost periodic solution p(p,,, t). It is further assumed that F(z, 1f, t) for a fixed p is almost periodic in t uniformly with respect to z in a cylindrical neighborhood of p(p,0, t) of radius ;r > 0.
openaire   +1 more source

Existence Theorems for Periodic Solutions and Almost Periodic Solutions

1975
First of all, we shall state some fixed point theorems without proofs. The following theorem is due to Brouwer. For the proof, see [5].
openaire   +1 more source

Rippled Almost Periodic Solutions

2022
Candace M. Kent, David M. Chan
openaire   +1 more source

Stability of Periodic or Almost Periodic Solutions

2018
In this chapter we study the asymptotic behavior of solutions as \({t } \rightarrow + \infty \), mainly in the case where \({h:}\ \mathbb {R} \rightarrow {H}\) is periodic or more generally almost periodic. As already mentioned in Remark 8.4.2, essentially nothing is known in this direction if f is non-linear.
openaire   +1 more source