Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order

Abstract

On the basis of properties of the Vejvoda-Shtedry operator, we obtain solvability conditions for the 2π-periodic problem

$$u_{tt} - u_{xx} = F\left[ {u,u_t } \right], u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0, u\left( {x,t + 2\pi } \right) = u\left( {x,t} \right)$$

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