An oscillation theorem for characteristic initial value problems for nonlinear hyperbolic equations

Abstract

The nonlinear hyperbolic operator L [ u ] ≡ u x y + c ( x , y , u ) L[u] \equiv {u_{xy}} + c(x,y,u) is studied and sufficient conditions are given that all solutions of the characteristic initial value problem for u L [ u ] ⩽ 0 uL[u] \leqslant 0 are oscillatory in ( 0 , ∞ ) × ( 0 , ∞ ) (0,\infty ) \times (0,\infty ) .