A pointwise oscillation property of semilinear wave equations with time-dependent coefficients
Under some assumptions on coefficients the author proves: If a solution \(u(x,t)\) to the equation \((a(t)u_t)_t-b(t)u_{xx}+c(t)u_t+d(t)u+f(t,u)=0, t>0,x\in (0,l)\) satisfying homogeneous boundary conditions does not identically vanish, then it oscillates, i.e. for any fixed \(x\), \(u(x,t)\) changes its sign infinitely many times on an infinite \(t\)-interval.
scientific article; zbMATH DE number 1975866