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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74441We 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.34 pages, 1 figureAnalysis of PDEs35C15; 35L05; 35L15Existence and blow up of small-amplitude nonlinear waves with a sign-changing potentialtext