Almost automorphic solutions represent a sophisticated generalisation of almost periodic functions and have become an increasingly influential concept in the study of differential equations. These ...

SIAM Journal on Applied Mathematics, Vol. 21, No. 3 (Nov., 1971), pp. 491-494 (4 pages) Let f(t,x,x') be locally Lipschitz continuous with respect to x and x'. Using differential inequality results, ...

In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator $\ddot{x}+f(\dot{x})+ax^{+}-bx^{-}=\varphi (t,x)$, where a and b are positive ...

Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...