on the periodic solutions of a class of nth order nonlinear differential equations *

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

The Existence and Uniqueness of Periodic Solutions for Some Nonlinear nth-Order Differential Equations

and Applied Analysis 3 Now, let f̃ : R 1 → R be a continuous function, T -periodic with respect to the first variable, and consider the nth-order differential equation u n f̃ ( t, u, u′, u′′, . . . , u n−1 ) . 2.5 Lemma 2.1 see 14 . Assume that the following conditions hold. i There exists ρ > 0 such that, for each λ ∈ 0, 1 , one has that any possible T -periodic solution u of the problem u n λf̃ ...

Anti-Periodic Solutions for a Class of Third-Order Nonlinear Differential Equations with a Deviating Argument

In this paper, we study a class of third-order nonlinear differential equations with a deviating argument and establish some sufficient conditions for the existence and exponential stability of anti-periodic solutions of the equation. These conditions are new and complement to previously known results.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Almost periodic solutions for a class of fourth-order nonlinear differential equations with a deviating argument

This work is concernedwith a class of fourth order semilinear ordinary differential equation with pseudo almost periodic environment and multiple delays. Specifically, we establish the existence and uniqueness of the pseudo almost periodic solutions. Furthermore, we discuss the global stability of the considered equation.

Anti-periodic solutions for a class of fourth-order nonlinear differential equations with variable coefficients∗

By applying the method of coincidence degree, some criteria are established for the existence of anti-periodic solutions for a class of fourth-order nonlinear differential equations with variable coefficients. Finally, an example is given to illustrate our result.