This paper is concerned with the oscillation of certain third-order nonlinear delay differential equations with damping. We give new characterizations of oscillation of the third-order equation in terms of oscillation of a related, well-studied, second-order linear differential equation without damping. We also establish new oscillation results for the third-order equation by using the integral...

They are of first order, second order, third order 27 and fourth order, respectively. The third-order Burg28 ers equation, similar to the second-order ones, appear 29 in many physical and engineering fields [8–10], such 30 as the plasma physics and fluid mechanics. In addi31 tion, these equations play a key role in nonlinear the32 ory and mathematical physics, in particular in the inte33 grable...

This work deals with the study of a compactness result for a class of pseudoparabolic problems of type: ∂tu− div{a(∂tu + E)∇(u + τ∂tu)} = 0. with boundary conditions that takes explicitly into account a nonlinear map of ∂tu.

Conditions are given on the nonnegative data «jc) and g{x, t) such that solutions of the pseudoparabolic inequality P[u] =» (L I)u, + Lu < 0 in Dx (0, t)