## Bounded, almost-periodic, and periodic solutions to fully nonlinear telegraph equations.(English)Zbl 0762.35066

The author considers the nonlinear partial differential equations of hyperbolic type: ${\mathcal L}u+F(u_{xx},u_ x,u,u_{tt},u_{xt},u_ t)=f(x,t),\quad x\in(0,L),\quad t\in\mathbb{R}^ 1,$ where $${\mathcal L}u=u_{tt}+du_ t-au_{xx}$$, $$a,d>0$$, together with the boundary conditions $$u(0,t)=u(L,t)=0$$.
The problem of existence of global in time solutions is studied. The existence theorem for the solutions belonging to the space of continuous functions is proved under some conditions on $$F$$ when $$f(x,t)$$ is sufficiently small. The existence theorems for periodic and almost- periodic solutions are proved when $$f(x,t)$$ is a periodic or almost- periodic function of $$t$$, respectively.

### MSC:

 35L70 Second-order nonlinear hyperbolic equations

### Keywords:

global in time solutions; existence theorem
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### References:

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