Fourth order wave equations with nonlinear strain and source terms ✩

In this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms. First we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions. Then we obtain a threshold result of global existence and nonexistence. Finally we discuss the global existence of solutions for the problem with critical initial condition I (u0) 0, E(0) = d. So the Esquivel-Avila’s results are generalized and improved. © 2006 Elsevier Inc. All rights reserved