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We show that blow up of solutions with arbitrary positive initial energy ofthe Cauchy problem for the abstract wacve eqation of the form $Pu_{tt}+Au=F(u)\ (*)$ in a Hilbert space, where $P,A$ are positive linear operators and$F(\cdot)$ is a continuously differentiable gradient operator can be obtainedfrom the result of H.A. Levine on the growth of solutions of the Cauchy problemfor (*). This result is applied to the study of inital boundary value problemsfor nonlinear Klein-Gordon equations, generalized Boussinesq equations andnonlinear plate equations. A result on blow up of solutions with positiveinitial energy of the initial boundary value problem for wave equation undernonlinear boundary condition is also obtained.

About Blow up of Solutions With Arbitrary Positive Initial Energy to Nonlinear Wave Equations