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## Energetic type estimates for singular hyperbolic equations of high order. (English)

Authors: Musteata A. T.

### Abstract

We study the equation $Pu+\lambda Qu=f(t,x,\lambda)$, $t>0$, $x\in R^1$, where $P$ and $Q$ are strictly hyperbolic operators whit variables coefficients of order $n$ and $n-1$ and $\lambda$ is a real parameter. We prove that if $P$ and $Q$ form a strictly hyperbolic pair then the solutions of this equation can be $a$ priori estimated uniform in $\lambda$.

Institutul de Matematică Academia de Ştiinţe
str. Academiei 5, MD-2028 Chişinău, Moldova