Forced Second-order Differential Equations Research Articles

New interval oscillation criteria for forced second-order differential equations with nonlinear damping

New interval oscillation criteria for forced second-order differential equations with nonlinear damping

Oscillations of a Class of Forced Second-Order Differential Equations with Possible Discontinuous Coefficients

We study the oscillation of all solutions of a general class of forced second-order differential equations, where their second derivative is not necessarily a continuous function and the coefficients of the main equation may be discontinuous. Our main results are not included in the previously published known oscillation criteria of interval type. Many examples and consequences are presented illustrating the main results.

Interval oscillation criteria for certain forced second-order differential equations

By using generalized Riccati transformations and an inequality due to Hardy et al., several new interval oscillation criteria are established for the nonlinear damped differential equation... The new interval oscillation criteria are different from most known ones in the sense they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. Our results improve and extend the known some results in the literature.

Interval oscillation criteria for a forced second-order nonlinear differential equations with damping

In this paper, we are concerned with the oscillations in a class of forced second-order differential equations with nonlinear damping terms. By using classical variational principle and averaging technique, several new interval oscillation criteria for the equations are established, which improve and extend some known results. Example is also given to illustrate the results.

Oscillation criteria for forced second-order nonlinear differential equations with damping

In this paper, we are concerned with oscillations in a class of forced second-order differential equations with nonlinear damping terms. By using a classical variational principle and an averaging technique, several new interval oscillation criteria for the equations are established, which improve and extend some known results. An example is also given to illustrate the results.

Interval oscillation criteria for a forced second-order differential equation with nonlinear damping

In this paper, we are concerned with the oscillations in a class of forced second-order differential equations with nonlinear damping terms. By using an inequality due to Hardy et al., several new interval oscillation criteria for the equations are established. These criteria are different from most known ones in that they are based on the information only on a sequence of subintervals of [ t 0 , ∞ ) , rather than on the whole half-line. Our results are more general, and extend the oscillation criteria of Wong and Yang. Examples are also given to illustrate the results.

Planar differential systems at resonance

We consider the system $$ J\dot u=\nabla { \mathcal {H}}(u)+f(u)+p(t)\,, $$ where ${ \mathcal {H}}:{{\mathbb R}} ^2\to{{\mathbb R}} $ is of class $C^1$ with locally Lipschitz continuous gradient, $f:{{\mathbb R}} ^2\to{{\mathbb R}} ^2$ is locally Lipschitz continuous and bounded, and $p:{{\mathbb R}} \to{{\mathbb R}} ^2$ is measurable, bounded and $T-$periodic. Here, $J= \begin{pmatrix} \scriptstyle 0 & \!\!\!\!\scriptstyle -1 \cr \scriptstyle 1 & \scriptstyle \!0 \end{pmatrix} $ is the standard symplectic matrix. For some classes of functions $f,$ we give new existence theorems for periodic solutions and for unbounded solutions. Applications are given to forced second-order differential equations with separated nonlinearities.