On some nonlinear hyperbolic <italic>p</italic>(<italic>x</italic>,<italic>t</italic>)-Laplacian equations.

This paper is devoted to study the global existence of solutions of the hyperbolic Dirichlet equation u t ⁢ t = L ⁢ u + f ⁢ ( x , t ) in ⁢ Ω T = Ω × ( 0 , T ) , <graphic></graphic> u_{tt}=Lu+f(x,t)\quad\text{in }\Omega_{T}=\Omega\times(0,T), where <italic>L</italic> is a nonlinear operator and ϕ ⁢ ( x , t , ⋅ ) {\phi(x,t,\cdot\,)} , f ⁢ ( x , t ) {f(x,t)} and the exponents of the nonlinearities p ⁢ ( x , t ) {p(x,t)} and μ ⁢ ( x , t ) {\mu(x,t)} are given functions. [ABSTRACT FROM AUTHOR]