Nonlinear Acoustics: Blackstock–Crighton Equations with a Periodic Forcing Term

Resonance in Undamped Second-order Nonlinear Equations with Periodic Forcing

where g and p are real valued functions continuous on the reals R , p(t+2n) = p(t), and the solutions of (1) are uniquely determined by their initial conditions. If g is nonlinear, the question of whether all solutions of (1) are bounded on R has long been recognized as nontrivial and challenging. For the special case of g(x) = 2x Morris [1] was able to show that this question has an affirmativ...

Almost Periodic Solutions of Second Order Nonlinear Differential Equations with Almost Periodic Forcing

2D Stochastic Navier-Stokes equations with a time-periodic forcing term

We study the long time behavior of the solution X(t, s, x) of a 2D-Navier-Stokes equation subjected to a periodic time dependent forcing term. We prove in particular that as t → ∞, E[φ(X(t, s, x))] approaches a periodic orbit independently of s and x for any continuous and bounded real function φ. 2000 Mathematics Subject Classification AMS: 76D05, 60H15,37A25

Nonlinear Difference Equations with Periodic Solutions

For ten nonlinear difference equations with only p-periodic solutions it is shown that the characteristic polynomials of the corresponding linearized equations about the equilibria have only zeros which are p-th roots of unity. An analogous result is shown concerning two systems of such equations. Five counterexamples show that the reverse is not true. Some remarks are made concerning equations...

Linear Differential Equations with Unbounded Delays and a Forcing Term

The paper discusses the asymptotic behaviour of all solutions of the differential equation ẏ(t) =−a(t)y(t) +∑ni=1 bi(t)y(τi(t)) + f (t), t ∈ I = [t0,∞), with a positive continuous function a, continuous functions bi, f , and n continuously differentiable unbounded lags. We establish conditions under which any solution y of this equation can be estimated by means of a solution of an auxiliary fu...