A POINTWISE OSCILLATION PROPERTY OF A SEMILINEAR WAVE EQUATION WITH A LOCALLY ODD AND INCREASING SEMILINEAR TERM

We shall consider a 1-dimensional semilinear wave equation in a finite interval (0, l). The semilinear term f(t, ·) is odd and increasing in a neighborhood of 0. We shall show that the solution u(x, t) oscillates on the time t, that is, let x be any fixed in (0,l), then u(x, t) changes its sign infinitely many times as t evolves.