Uniqueness theorem for quasilinear 2nth-order equations

We are concerned with existence and uniqueness of the solution of initial value problems for quasilinear 2nth-order equations of the type (−1)n |u(n)|p−2u(n) (n) = λ|u|q−2u, where n ∈ N, λ ∈ R and p, q > 1. We show that there exists a global solution for p q, while the solution can “blow-up” for p q we give an example of nonuniqueness. We prove the uniqueness theorem for a general equation, involving nonconstant coefficients and jumping nonlinearity.  2004 Elsevier Inc. All rights reserved