Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential

[摘要] We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of small-amplitude solutions is driven by the nonlinear term. If the potential induces growth in the linearized problem, however, solutions that start out small may blow-up in finite time. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2005-12-15

[关键词] wave equation;radially symmetric;small-amplitude solutions