Uniqueness theorem for quasilinear 2nth-order equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:293

Article

Benedikt, J

关键词: existence and uniqueness of solution;    continuous dependence on initial conditions;    jumping nonlinearity;   

DOI  :  10.1016/j.jmaa.2004.01.021

来源: Elsevier

【 摘 要 】

We are concerned with existence and uniqueness of the solution of initial value problems for quasilinear 2nth-order equations of the type [GRAPHICS] where n is an element of N, lambda is an element of 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. On the other hand, there is at most one solution for p less than or equal to q, and for p > q we give an example of nonuniqueness. We prove the uniqueness theorem for a general equation, involving nonconstant coefficients and jumping nonlinearity. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free