FORCED OSCILLATIONS OF NONLINEAR HYPERBOLIC EQUATIONS WITH FUNCTIONAL ARGUMENTS
Main Article Content
Abstract
In this paper, sufficient conditions for the forced oscillations of hyperbolic equations with functional arguments of the form
\[\frac{\partial^2}{\partial t^2}=a(t)\Delta u(x, t)+\sum_{i=1}^m a_i(t)\Delta u(x, \rho(t))-\sum_{j=1}^k q_j(x, t)f_j(u(x, \sigma_j(t)))+f(x, t) \]
$(x, t)\in\Omega\times[0, \infty)$ are obtained, where $\Omega$ is a bounded domain in $\mathbb{R}^n$ with piecewise smooth boundary $\partial\Omega$ and $\Delta$ is the Laplacian in Euclidean $n$-space $\mathbb{R}^n$.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
B. T. Cui, Oscillation theorems of hyperbolic equations with deviating arguments, Acta Sci Math. (Szeged) 58(1993), 159-168.
B. S. Lalli, Y. H. Yu and B. T. Cui, Oscillatzons o with dcviating arguments, Bull. Austral. Math. f certain neutral differential equations
B. S. Lalli, Y. H. Yu and B. T. arguments, Appl. Math. Cornput. 53(1993), 97-110 Soc. 46(1992), 373-380. Cui, Oscillation of hyperbolic equations with functional
D. D. Bainov and B. T. Cui, Oscillation properties for damped hyperbolic equations with deviating arguments, in Proceedings of The Third International Colloquium on Differential Equations, International Science Pubishers, 1993, 23-30(Netherlands).
B. S. Lalli, Y. H. Yu and B. T. Cui, Forced Oscillations of hyperbolic differential equations with deviating arguments Indian. J. Pure Appl. Math. 25(1994), 387-397
B. T. Cui, 0scillation properties of the solutions of hyperbolice eqitations with deviating arguments, Dernonstratio Mathematica 29(1996), 61-68.
N. Yoshida, Forced oscillations of solutions 0f parabolic equations, Bull. Austral. Math. Soc. 36(1987), 287-294.
B. T. Cui, Oscillation theroems of nonlinear parabolic equations of neutral type, Math. J Toyama Univ. 14(1991), 112-123