On potential wells and vacuum isolating of solutions for semilinear wave equations (Q1399887)

The author studies the initial boundary value problem of semilinear wave equation \(u_{tt}-\triangle u=|u|^{p-1}u\) on a bounded domain. He introduces a family of potential wells which include the known potential well as a special case, to prove existence and nonexistence theorems of global solutions for the problem.