We study a class of functional differential equations x(t) = af(x(t 1)) with periodic nonlinearity /: R -> R, 0 < / in ( A, 0) and / < 0 in (0, B ), /( A ) = /(0) = /( B) = 0. Such equations describe a state variable on a circle with one attractive rest point (given by the argument £ = 0 of/) and with reaction lag a to deviations. We prove that for a certain critical value a = a0 there exists a...

Abstract This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it shown that, any measurable bounded function f , the time average $\frac{1}{t} \int_0^t f(X_s)ds$ converges in $\mathbb{L}^2$ towards limiting distribution, starting from initial distribution process $...

and Applied Analysis 3 the hull of f . It is easy to see that if f n is almost periodic, then for all f1 ∈ H f , lim inf n→∞ f n inf n∈Z f n inf n∈Z f1 n , lim sup n→∞ f n sup n∈Z f n sup n∈Z f1 n . 1.7 Definition 1.2. Let f : Z × C → R. Then f is said to be almost periodic in n ∈ Z uniformly on compact set of C, if f n, · is continuous for each n ∈ Z, and for any > 0 and every compact setK ⊂ C...

We prove a result of Ambrosetti–Prodi type for the scalar periodic ODE x?=f(t,x)?s, where, seemingly first time in literature, f(?,x) is allowed to have indefinite sign as |x|?+?. Our requires that f satisfies one-sided growth control; case such control fails, non-existence occurs large s>0, although multiplicity solutions can still be detected provided f(?,0)=0 and s>0 small enough.

In this paper the degree of approximation function f, which is periodic with respect to hexagon lattice by matrix means T(A)n(f) its hexagonal Fourier series in generalized H?lder metric, where A a lower triangular infinite nonnegative real numbers nonincreasing row estimated.

Accurate detection of weak periodic signals within noise and possibility of secure messaging have made Duffing oscillator (DO) highly important in the field of communication. Investigation on the properties of DO is thus ardently sought for. An elegant approach to accomplish the same is to fabricate electronic circuit simulating DO non-linear equation and to study the effect of input signal amp...

Let H̃r ∞,β denote those 2π-periodic, real-valued functions f on R, which are analytic in the strip Sβ := {z ∈ C : |Im z| < β}, β > 0 and satisfy the restriction |f (r)(z)| ≤ 1, z ∈ Sβ . Denote by [x] the integral part of x. We prove that the rectangular formula QN (f) = 2π N N−1 ∑

The existence of periodic solutions for the evolution equation y′(t) + Ay(t) 3 F (t, y(t)) is investigated under considerably simple assumptions on A and F . Here X is a Banach space, the operator A is m-accretive, −A generates a compact semigroup, and F is a Carathéodory mapping. Two examples concerning nonlinear parabolic equations are presented.

In this talk, we deal with the representation of a 2π-periodic function f by a trigonometric series

where f is a given continuous function in R 3 and f is T-periodic in t and s. Periodic solutions of nonlinear hyperbolic partial differential equations have been studied extensively in the recent years [1, 6, 7, 8, 9, 10, 11, 12, 13, 14]. The two approaches that have been used are: (i) reduction to an alternative problem and (ii) the Galerkin method and passage to the limit through a sequence o...