Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations

Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations

The study on periodic solutions for ordinary differential equations is a very important branch in the differential equation theory. Many results about the existence of periodic solutions for second-order differential equations have been obtained by combining the classical method of lower and upper solutions and the method of alternative problems The Lyapunov-Schmidt method as discussed by many ...

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

Existence and uniqueness results for a nonlinear differential equations of arbitrary order

This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.

Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations

The authors study the existence and uniqueness of a set with 2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a limit point of the above set of 2kT-periodic solutions.

Existence and uniqueness of periodic solutions of second-order nonlinear differential equations

This paper is concerned with the following second-order nonlinear differential equation: x (2n) (t) + n+1 k=1 f k (x (k–1) (t))x (k) (t) – g(t, x(t)) = e(t). By applying Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence and uniqueness of periodic solutions for the above equation. Some recent results are known as the special cases of...