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Oscillatory criteria of general nonlinear hyperbolic equations with continuous deviating arguments. (English) Zbl 1028.35153
The authors use averaging technique to study oscillatory properties of the following nonlinear hyperbolic equation \[ \frac{\partial^2}{\partial t^2}[u + \lambda(t)u(x,t-\tau)] = a(t)\Delta u - c(x,t,u) - \int_a^b q(x,t,\xi)f(t,u(x,g(t,\xi))) d \sigma (\xi), \] together with boundary conditions of Dirichlet or mixed type. Sufficient conditions for the oscillation of the solutions are obtained.

MSC:
35R10 Partial functional-differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35L70 Second-order nonlinear hyperbolic equations
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