By using averaging functions, new interval oscillation criteria are established for the second-order functional differential equation, (r(t)l~'(t)l~-l~'(t))'+t,~(t,~(t),~(~-(t)),~'(t),~'(,-(t)))=o, t>to, that are different from most known ones in the sense that they are based on information only on a sequence of subintervals of [to, oo), rather than on the whole half-line. Our results can be applied to three cases: ordinary, delay, and advance differential equations. In the case of half-linear functional differential equations, our criteria implies that the T(t) < t delay and v(t) >__ t advance cases do not affect the oscillation. In particular, several examples are given to illustrate the importance of our results. (~) 2005 Elsevier Ltd. All rights reserved.

This paper gives a priori estimates and continuous dependence of the solutions to fourth-order nonlinear wave equation.

In this paper the initial-boundary value problem for a nonlinear strongly damped wave equation is considered.We analyze the structural stability of solutions of the nonlinear strongly damped wave equation with coefficients from H 1 (Ω) .