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

• Date: 1998
• Main Authors: Mitropolskiy, Yu. A., Khoma, N. H., Khoma, G. P., Митропольский, Ю. А., Хома, H. Г., Хома, Г. П.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1998
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4892
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

On the basis of properties of the Vejvoda-Shtedry operator, we obtain solvability conditions for the 2π-periodic problem $$u_{tt} - u_{xx} = F\left[ {u,u_t } \right], u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0, u\left( {x,t + 2\pi } \right) = u\left( {x,t} \right)$$ .