Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 22, No 2, (1996), 125p-164p
In this work we study the existence of global solution to
the semilinear wave equation (1.1) (∂2t − ∆)u = F(u),
where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace
operator on R^n.
The existence of solutions with small initial data, for the case of space dimensions
n = 3 was studied by F. John in , where he established that for 1 < λ < 1+√2
the solution of (1.1) blows-up in finite time, while for λ > 1 + √2 the solution exists
globally in time. Therefore, the value λ0 = 1 + √2 is critical for the semilinear wave
∗The author was partially supported by Alexander von Humboldt Foundation and the Contract
MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.