Periodic Solutions with Minimal Period for Fourth-Order Nonlinear Difference Equations

Periodic Solutions for Some Fully Nonlinear Fourth Order Differential Equations

In this paper we present sufficient conditions for the existence of solutions to the periodic fourth order boundary value problem u(x) = f(x, u(x), u′(x), u′′(x), u′′′(x)) u(a) = u(b), i = 0, 1, 2, 3, for x ∈ [a, b], and f : [a, b] × R4 → R a continuous function. To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations w...

Periodic solutions for nonlinear second-order difference equations

We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f :R→ R is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant β > 0 such that u f (u) > 0 whenever |u| ≥ β. For such an equation we prove that ifN is an odd integer...

Existence of Periodic Solutions for Higher-order Nonlinear Difference Equations

In this article, we study a higher-order nonlinear difference equation. By using critical point theory, we establish sufficient conditions for the existence of periodic solutions.

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

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...