# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [1] Mishev, D.P., Oscilatory properties of the solutions of hyperbolic differential equations with “maximum”, Hiroshima math. J., 16, 77-83, (1986) · Zbl 0609.35054 [2] Mishev, D.P.; Bainov, D.D., Oscilation properties of the solutions of a class of hyperbolic equations of neutral type, Funkcial ekvac., 29, 2, 213-218, (1986) · Zbl 0651.35052 [3] Yoshida, N., On the zeros of solutions of hyperbolic equations of neutral type, Diff. integr. eqs., 3, 155-160, (1990) · Zbl 0749.35006 [4] Cui, B.T.; Lalli, B.S.; Yu, Y.H., Forced oscillations of hyperbolic differential equations with deviating arguments, Acta math. appl. sinica., 11, 4, 369-377, (1995) · Zbl 0853.35126 [5] Li, Y.K., Oscillation of systems of hyperbolic differential equations with deviating arguments, Acta math. sinica., 40, 1, 100-105, (1997) · Zbl 0881.34079 [6] Fu, X.L., Oscillation of a class of parabolic partial differential equations, Acta math. sci., 13, 3, 316-322, (1993) [7] Yu, Y.H.; Fu, X.L., Oscillation of second order nonlinear neutral equations with continuous distributed deviating arguments, Rad. mat., 7, 1, 167-176, (1991) [8] Wong, P.G.; Fu, X.L.; Yu, Y.H., Oscillation of a class of delay hyperbolic equations, J. math. res. exposion., 18, 2, 105-111, (1998) [9] Vladimirov, V.S., Equations of mathematical physics, (1981), Nauka Moscow · Zbl 0485.00014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.